Question
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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)
Hint:
, where a and b can be real values, variables or multiples of both. We are asked to use polynomial identities to simplify the given expressions.
The correct answer is: lowest form.
Step 1 of 2:
The given expression is
. It can be written as
. It is of the form
where ![a equals 1 fourth x cubed straight & b equals 5 y squared](data:image/png;base64,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)
Step 2 of 2:
Use the polynomial identity to simplify the expression;
![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 open parentheses 1 over 16 x to the power of 6 minus 25 y to the power of 4 close parentheses equals open parentheses 1 fourth x cubed close parentheses squared minus open parentheses 5 y squared close parentheses squared end cell row cell equals open parentheses 1 fourth x cubed minus 5 y squared close parentheses open parentheses 1 fourth x cubed plus 5 y squared close parentheses end cell end table](data:image/png;base64,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)
Thus, the factor form is ![open parentheses 1 over 16 x to the power of 6 minus 25 y to the power of 4 close parentheses equals open parentheses 1 fourth x cubed minus 5 y squared close parentheses open parentheses 1 fourth x cubed plus 5 y squared close parentheses](data:image/png;base64,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)
Thus, the factor form is
We can use multiple identities to factorize an expression. Our aim is to reduce the expression into the lowest form.
Related Questions to study
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,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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 :
![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 :
![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,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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 :
![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,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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 : ![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,iVBORw0KGgoAAAANSUhEUgAAAM4AAAATCAYAAADYvzI1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAvFJREFUeNrtmtGHVFEcx4+xVpIlWSs9xFhJ1lrSw1rpJWslY0UyslZiJSur9/SQWD3sU2/pIUkkSdZa0kPGWpGstQ8r+hd66CEZcfqdme9wXOfeOefeuXfO+XW+fJk7c2fm972fOXd+59wrhJ+ScJu8Q54UPMQhV2QTgGrku+Rvgpc45IpsNKk3rHsY5o/gKT3XOo5/ZBMYm2nyrocBLpE/MwRjyrUDDpFNOGw6L8xo23Pkt+Rf6Pv2yDczekOTi+ok6qqXeJDOkB8gn6goX1qu8+RWZBMOmxnsrEuNuCb5GLbPYZ+mofiyDtomgpSpl+SVjByy4lwtQIps/GcjnpBXLT74NHm/Ajiq8C3yWMWrKmXDscl1LzGX4cRGMmMjtskXc04GXYq/nTLBfYTXelIBzlbc1xaF85x8w/D8GvmxQ65Z8iembCQzNp1eedSigFlD2+B6MNQy34S2fYv81KJ39X3gLOPfQddR8nfyCYdco+DBkY1kxkb8tfjyI+QvmJgmi2/jA9Wova/13iYtkDfw+HJyBA9RWXBs8l0hv0k89xCTW1e1mbKRzNj0hXOc/J48n7HPCCZOqpjDPn97H0V3yW9PG/FFYPTzIKD2y6dyHGjb4+Qf+FGXOXAim+GxyWwH6gDjcgvCvMhe319DAdPCH8kB5PutPd5ATle5tGqhsZHM2HTOMnOGHdXIfYZ+0FVpV5R71yBU8c1AB05avhZ+zHWc0Wo56khOQDmxkczYGJc8J9AXjuT4gikUZzpDfgBs1Yt+HUA7MAyoaflekBvkV+SlnHWsJiaynNhIZmyMF9k2hd2y4zuMxBq8gMKvJfYbxwROh3FVdC9y+TxwbPP12hy19LlfoA6bC6ChspHM2HS0m+hrbSd010V3WU9NYn/iTHjB0BuqkKcMxbxG4GEOmKL5elrE+xs5a0m75Say8ZeNtzcShqRGwWMY2k2ekQ10R/h563oo2kLrkEeqd17JeD2y8ZdNVAFNYe4R9R+w+Qc6nZUgRKn1wAAAAWh0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bW4+MjU8L21uPjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjE1PC9tbj48bXN1cD48bWk+eTwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21yb3c+PC9tZmVuY2VkPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtbj4yNTwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtbj4xNTwvbW4+PG1zdXA+PG1pPnk8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tcm93PjwvbWZlbmNlZD48L21hdGg+mWxj0gAAAABJRU5ErkJggg==)
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.
Use polynomial identities to multiply the expressions ? (10 + 21)2
Algebraic expression is an expression that is built by the combination of integer constants and variables.
Use polynomial identities to multiply the expressions ? (10 + 21)2
Algebraic expression is an expression that is built by the combination of integer constants and variables.
Use polynomial identities to multiply the expressions ? (7 + 9)2
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
Use polynomial identities to multiply the expressions ? (7 + 9)2
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
Use polynomial identities to multiply the expressions ? 103
97
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 ? 103
97
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 ? 18
22
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
Use polynomial identities to multiply the expressions ? 18
22
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
Use polynomial identities to multiply the expressions ? ![open parentheses 6 minus y cubed close parentheses squared](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 6 minus y cubed close parentheses squared](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 8 minus x squared close parentheses open parentheses 8 plus x squared close parentheses](data:image/png;base64,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)
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.
Use polynomial identities to multiply the expressions ? ![open parentheses 8 minus x squared close parentheses open parentheses 8 plus x squared close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAASCAYAAACD3FoaAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAgxJREFUeNrtmb9Lw0AcxY8iGURcREQcBBERh1JwEhEpODg4iODgKIIUKeL/IEIRcSiuTiIu4iAigohIKUUQcXJzcnAXBwnC+b3wquG4S1qTK5fEBw/S/Djy4S7fe3dlLHnisEuuk0dZupR2vh/lyBvkx3++X4kHKgkD/fQdV8CQSb48uZEwuFnynXSuDpas8XkXCtK5bnKV/IGRcEUesgRuEO88Ip2fJNeyxlfAzbIOyTvkLrKDT/jeArgx8gUgVaoBNCt8bJdcDqm/zYnVtWBkXpJ7A+7ZlOY6U3zcEj6vdMwobhSlpUcCfDXUMWuagLGNa00JuPGQtqbINx3g45bwsXeUEFlV9Lb/wT2DX5eIzAO+36vkA806yW9ZDphM83FL+NhXQDJ1YZGG3jQjOS7Nk/dxPCePsjbldoCPW8KnBBwmH6MmO74E9KKLsZrREzaaZF0jPj+R+wx2YJr4lCXmTANSJN8a/Aq38HL5CG20UkLj4OOW8HmjYjokobV6LYrEO5yizKxEaEee5E3xcUv4lDH7mak3UicwV8QtsWA9x+JaJMOHCCWmDCbTfNwSPuVCdwmQRcTrHI7FHFGKufP6EZ/9QAvkoz+218pCPg4+bgmfp4aiLi8j+rooKyKpLcbceQ7mI9UW1gmSWzvSbaWlnS+Rm70qpWkzux0+TyWWvL9b5Ll8PeB66vi+AWRU1CN+6EEsAAABDnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtbj44PC9tbj48bW8+JiN4MjIxMjs8L21vPjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48L21mZW5jZWQ+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1yb3c+PG1uPjg8L21uPjxtbz4rPC9tbz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21yb3c+PC9tZmVuY2VkPjwvbWF0aD5UXVHeAAAAAElFTkSuQmCC)
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.