Question
Use the binomial theorem to expand the expressions: ![left parenthesis 2 a minus b right parenthesis to the power of 5](data:image/png;base64,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)
Hint:
The binomial expansion is
, here n ≥ 0 . We are asked to find the expansion of
using Binomial theorem.
The correct answer is: triangle
Step 1 of 2:
The given expression is
where n=5. So, we would have 5+1=6 terms in the expansion. The values of
.
Step 2 of 2:
Substitute the values in the binomial equation to get the answer:
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell left parenthesis 2 a minus b right parenthesis to the power of 5 equals 5 C subscript 0 left parenthesis 2 a right parenthesis to the power of 5 plus 5 C subscript 1 left parenthesis 2 a right parenthesis to the power of 4 left parenthesis negative b right parenthesis plus 5 C subscript 2 left parenthesis 2 a right parenthesis cubed left parenthesis negative b right parenthesis squared plus 5 C subscript 3 left parenthesis 2 a right parenthesis squared left parenthesis negative b right parenthesis cubed plus 5 C subscript 4 left parenthesis 2 a right parenthesis left parenthesis negative b right parenthesis to the power of 4 plus 5 C subscript 5 left parenthesis negative b right parenthesis to the power of 5 end cell row cell equals 32 a to the power of 5 plus 5 open parentheses 16 a to the power of 4 close parentheses left parenthesis negative b right parenthesis plus 10 open parentheses 8 a cubed close parentheses open parentheses b squared close parentheses plus 10 open parentheses 4 a squared close parentheses open parentheses negative b cubed close parentheses plus 5 left parenthesis 2 a right parenthesis open parentheses b to the power of 4 close parentheses plus left parenthesis negative b right parenthesis to the power of 5 end cell row cell equals 32 a to the power of 5 minus 80 a to the power of 4 b plus 80 a cubed b squared minus 40 a squared b cubed plus 10 a b to the power of 4 minus b to the power of 5 end cell end table](data:image/png;base64,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)
Thus, the expansion is ; ![left parenthesis 2 a minus b right parenthesis to the power of 5 equals 32 a to the power of 5 minus 80 a to the power of 4 b plus 80 a cubed b squared minus 40 a squared b cubed plus 10 a b to the power of 4 minus b to the power of 5](data:image/png;base64,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)
Thus, the expansion is ;
The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.
Related Questions to study
Use the binomial theorem to expand the expressions: ![left parenthesis x plus 3 right parenthesis cubed](data:image/png;base64,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)
The answer can also be found using the Pascal’s triangle (using the fourth row).
Use the binomial theorem to expand the expressions: ![left parenthesis x plus 3 right parenthesis cubed](data:image/png;base64,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)
The answer can also be found using the Pascal’s triangle (using the fourth row).
Use polynomial identities to factor the polynomials or simplify the expressions : ![8 cubed minus 2 cubed](data:image/png;base64,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)
Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.
Use polynomial identities to factor the polynomials or simplify the expressions : ![8 cubed minus 2 cubed](data:image/png;base64,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)
Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.
Use polynomial identities to factor the polynomials or simplify the expressions :
![10 cubed minus 3 cubed](data:image/png;base64,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)
Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.
Use polynomial identities to factor the polynomials or simplify the expressions :
![10 cubed minus 3 cubed](data:image/png;base64,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)
Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.
Use polynomial identities to factor the polynomials or simplify the expressions :
![10 cubed plus 5 cubed](data:image/png;base64,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)
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.
Use polynomial identities to factor the polynomials or simplify the expressions :
![10 cubed plus 5 cubed](data:image/png;base64,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)
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.
Use polynomial identities to factor the polynomials or simplify the expressions :
![9 cubed plus 6 cubed](data:image/png;base64,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)
Polynomial identities are used to simplify or to find the product of expressions. It reduces space and time during solving.
Use polynomial identities to factor the polynomials or simplify the expressions :
![9 cubed plus 6 cubed](data:image/png;base64,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)
Polynomial identities are used to simplify or to find the product of expressions. It reduces space and time during solving.
Use polynomial identities to factor the polynomials or simplify the expressions :
![open parentheses 1 over 16 x to the power of 6 minus 25 y to the power of 4 close parentheses](data:image/png;base64,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)
We can use multiple identities to factorize an expression. Our aim is to reduce the expression into the lowest form.
Use polynomial identities to factor the polynomials or simplify the expressions :
![open parentheses 1 over 16 x to the power of 6 minus 25 y to the power of 4 close parentheses](data:image/png;base64,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)
We can use multiple identities to factorize an expression. Our aim is to reduce the expression into the lowest form.
Use polynomial identities to factor the polynomials or simplify the expressions :
![64 x cubed minus 125 y to the power of 6](data:image/png;base64,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)
Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.
Use polynomial identities to factor the polynomials or simplify the expressions :
![64 x cubed minus 125 y to the power of 6](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGcAAAATCAYAAACN8hMuAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAttJREFUeNrtWE9kXEEYf9ZasSrEWlE9hBWxaq1QERXRS0RURYWoiqoIOUQP0Xv1UKV62FMvUTlURIhaVbVK9RARUVZEVUXoIYccIuQQFWuV9Pv4LZ/pzO7My3vdYffHj32z7837Zr5/v3lB0H5cgnXiPnEy6DyMEreINbEf3iFPPOowx9wk7hELvhuaIJ51mHPeEcd9NzJDfEOc7zDnnBLnUDEOibOmG0eIm8Rz1L+PxDtNJr4XUX1s1NlHMW/EEPEZepsOY8T3WH+jB841sVdHV/whviX2ElP4/U+ALsIZQ7juhWHbhkmvEX9G2Lz4fS9hR1xYw/wmm7kpP8TaGv1gB2Oqc6LCIcq53NcjtSlVHSddIS7EoCxq/0kh2mKA+D1G53Cm9InrlOqLFU10NAOn/9cWhrLjXmnGX+A/HcZDBEncztEFjO3zq8QHmvFlVAlGEaKAK0cSfXdK3nxAvG75whQiacDCUJaI/eJ6Hi/X1W/egM9iXl+ccxulLczzj4mvlbE0SllGjHH7+EU80QmCGnpNmXiBZlg1NEPOhieWhnIElPB7QmSbDwdfG/QQv6FSqM/XIRwqxKeiT0nchcCSeA5R4mTsHiZLokGNwcNL4r5iiCj6AsW3r0TLVVTdVdWSzX3cBz60+GLBe3ULm32AQ7R6PPghrrPIkB6XRXME3NCMDxOPxTVH0aDjQpcRZUWPzhatbM7BMYMOc05C7am4EL9L2A8nVBQ5J1F3iFzTuaHkKDja6Zw8FFQ6IqW5DWfnkDUJ10mXDKoij2wJs9Aczk1p1ONqBGUtbuf0o0ckQ8xZwObrPs9ME9fDHrJTSMkFYdgoVNlEiIVmkY0Z5WvCmufO+aTpGzqUoeIS4BQcM2Mo66uas5ITskjn3/iksBXYfZC71Di6bOhhG6qGb4NTmpVi25I9C7HE+3SGbBsxvPM+np8OuvAO7JTd7jb4iQpKYBeeoYA+Fgp/ARl+yL1zZP9rAAAAqXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbj42NDwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4zPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTI1PC9tbj48bXN1cD48bWk+eTwvbWk+PG1uPjY8L21uPjwvbXN1cD48L21hdGg+M6qY8gAAAABJRU5ErkJggg==)
Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.
Use polynomial identities to factor the polynomials or simplify the expressions :
![216 plus 27 y to the power of 12](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFwAAAATCAYAAAAd4WrhAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAitJREFUeNrtV8FHREEcfp6VrESyVjrEWmulw16SJIl02EO6rKwkiZU97T+QTl06dE86JIkkydp7VhIrWR2ydOzQNVlrxes3fIfnmbdvZt7M6/I+PvbNjLfffPOb3+/3LCuGKnLEfeIrZ84B+8RHYja2KzwuiBUY6webWCW+xHbpgyOwphfbFJ3hS8QH7+AC8Yb4jbzD8tKmYv5yY5Z4jfeyU76HAJ0Q1e4E0IThE8jhGe8EO4EycQTP01hYDpG/KjA4h+dRGNHUbLisdi9KxFMDhrN912G6EKaIbcU/Y5tuRZAbw2hnSCMAhjXrZCY3EGRS6CmaciIRYSYMFy1U7AYWPGNnxA3O2hrxUFAnMzsvK3geV1PFlHeZq2TAcBHte6hDXmwTjzxjSWKHOB5QE0TmuGBX7BkFScWUHnLYLbGLYtYKKMS6DBfRPoU1Cc5cEYXejQOfw9GCMeIdcTWEKQ6a/SI2ZcOADj4ELIUuwtGonRXaZZ85FsVvrucU8SNknvdFBoKzIaOQtWiTnHGWLz8NRbio9hJy7CB0Xb+Pkb+1I4/2KKnh2jcQ1Tz0DRguqt1GfSkErGviADOIblu32WnkrYSmwlb1qfR55E6dhstoX+d99XFwTlwjXhK3TER3XaWNGWDKEDa26zJiDr3ximbDZbRfEXcE1tXQHrYtQ5AtVCLrUrjmP8RfHMDiP2v/QmEVuQkOojxGBGBGP8U2RIcGPp5iRIAZ1AUj+ANBkK+WPOsIzgAAAIJ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW4+MjE2PC9tbj48bW8+KzwvbW8+PG1uPjI3PC9tbj48bXN1cD48bWk+eTwvbWk+PG1uPjEyPC9tbj48L21zdXA+PC9tYXRoPl4oa1YAAAAASUVORK5CYII=)
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.
Use polynomial identities to factor the polynomials or simplify the expressions :
![216 plus 27 y to the power of 12](data:image/png;base64,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)
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.
Use polynomial identities to factor the polynomials or simplify the expressions :
![4 x squared minus y to the power of 6](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD8AAAATCAYAAAAnMdWSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAcJJREFUeNpjYKAd+A/Fv4D4KBCrMAwcMAfig0D8A8lddAFMQJwFxOcGyONaULt1BjDwwaE+EGAhENsOpMftocluIMBrII4G4odAfAuIQwlp8KFivpCE5nmlAfL8HyCeDcR8QMwGZSfiUswDxNeo5Hk1IN4CDYCBAreg5Q6y/x7iUjwTiJOp4HmQh7dBQ3wgASimBZH4oNg/g02hNRDvRaqqsAFQwHRgEW+GysEAyOMaNPbYXCAOxyJeAMStULYetNADRQILEE8BYg90DaAQuQTE8gQ8zwCtOsSR+IlQQ7HV8/9pWLfGA3EXmhgXNKkLI4mBCry7QPwSV4EHis0cNMfjAqCQ64OyXZBSC72BFxCvQhOrB+JaUgzRg5bIDER6HgR2Q6uwC2ihTElrEB/GBkD2XkHii0JjmIMUy09iaX4S8nwBtOmqN8AF2jckdh/UXVQNeWwF4xqoZZED7PnD0DaEEjTWmajVMcEGQJZsghYsPNBqQ3gAPQ8qyf2AeCkQx1KzV4YORKFVmDBaa3DxAHq+AFrlXaJ2lxS9KlwHxNJY1C7HVnfSCQRA3erHMAIByNPHGUYoAGVDy5HocR1ox4ksAAARiGnTBjvoPQAAAJx0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW4+NDwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bXN1cD48bWk+eTwvbWk+PG1uPjY8L21uPjwvbXN1cD48L21hdGg+8/qD2AAAAABJRU5ErkJggg==)
Polynomial identities are used to simplify or to find the product of expressions. It reduces space and time during solving.
Use polynomial identities to factor the polynomials or simplify the expressions :
![4 x squared minus y to the power of 6](data:image/png;base64,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)
Polynomial identities are used to simplify or to find the product of expressions. It reduces space and time during solving.
Use polynomial identities to factor the polynomials or simplify the expressions : ![x cubed minus 27 y cubed](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAATCAYAAADcZiBNAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAclJREFUeNpjYCAd/IfiX0B8AYjdGIYHoJm/NID4IcPwA1T1FxMQvxuGgUQ1fwkD8RQgThxmAUQ1f8HybyyNHGoNxGuA+BNSGRGNxx248ID7iw+IW4E4jQaBdBCII4GYB8rXAuKjUDFiQCgQzx5M/vpBp2wgD8SXiFAnDsSHgZiDFv5KBuIOLOLNUDlswBaIz9CxvCAmQjYBsQGa2FwgDseitgCaakjy1zloTMBAIrQQw5ZvQQ7eAY1hegBLaJbDBzKAuBaLeDwQd6GJcQHxLWhBTZK/PIC4D8p2AeK9g6TGAWWdk9ACHV92BKlhwSLnBcSr0MTqcQQoUWA3ENtDaxRhKtWClNRAgkC8gYgWMKiwd8RTrV9B4osC8V1Kyq0CaLWrNwhSkBI0gFSIqM22EVDzDYndB/UnRe2TPhKqW1p2DWZDyw5CreMbWAprdHAYGuhK0FTERG6sbYI6igdaugsPUACJQ8sQFiLUBkCzGiGwEIj9gHgpuY1FUWhyRQ4UHyBePECBtAWakogBy4nsQhRAmwKXyHEQGxCvA2JpHA7wGMBhC2IK+pfQwp2YFPcfmppGAQ4ACpzjo8GAH2yDNkhHAQ6gAy3nyAIATxJ1oljiS+EAAACddEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1pPng8L21pPjxtbj4zPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW4+Mjc8L21uPjxtc3VwPjxtaT55PC9taT48bW4+MzwvbW4+PC9tc3VwPjwvbWF0aD5Gqg6sAAAAAElFTkSuQmCC)
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants
Use polynomial identities to factor the polynomials or simplify the expressions : ![x cubed minus 27 y cubed](data:image/png;base64,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)
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants
Use polynomial identities to factor the polynomials or simplify the expressions : ![8 x cubed plus y to the power of 9](data:image/png;base64,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)
Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.
Use polynomial identities to factor the polynomials or simplify the expressions : ![8 x cubed plus y to the power of 9](data:image/png;base64,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)
Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.
Use polynomial identities to factor the polynomials or simplify the expressions : x9 - 8
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions
Use polynomial identities to factor the polynomials or simplify the expressions : x9 - 8
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions
Use polynomial identities to factor the polynomials or simplify the expressions : x8 - 9
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.
Use polynomial identities to factor the polynomials or simplify the expressions : x8 - 9
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.
Use polynomial identities to multiply the expressions ? ![open parentheses 25 x squared minus 15 y squared close parentheses open parentheses 25 x squared plus 15 y squared close parentheses](data:image/png;base64,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)
Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.
Use polynomial identities to multiply the expressions ? ![open parentheses 25 x squared minus 15 y squared close parentheses open parentheses 25 x squared plus 15 y squared close parentheses](data:image/png;base64,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)
Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.
Use polynomial identities to multiply the expressions ? ![open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses](data:image/png;base64,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)
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.
Use polynomial identities to multiply the expressions ? ![open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses](data:image/png;base64,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)
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.