Question
Use polynomial identities to factor each polynomial : ![m to the power of 9 plus 27 n to the power of 6](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 factor the given polynomial.
The correct answer is: higher degree polynomial expressions.
Step 1 of 2:
The given expression is
. It can be written as
. This is of the form
where
.
Step 2 of 2:
Substitute the values in the expansion to get the factor form. Thus, we get:
![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 m to the power of 9 plus 27 n to the power of 6 equals open parentheses m cubed close parentheses cubed plus open parentheses 3 n squared close parentheses cubed end cell row cell equals open parentheses m cubed plus 3 n squared close parentheses open parentheses open parentheses m cubed close parentheses squared minus open parentheses m cubed close parentheses open parentheses 3 n squared close parentheses plus open parentheses 3 n squared close parentheses squared close parentheses end cell row cell equals open parentheses m cubed plus 3 n squared close parentheses open parentheses m to the power of 6 minus 3 m cubed n squared plus 9 n to the power of 4 close parentheses end cell end table](data:image/png;base64,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)
The factor of the expression is,
.
The factor of the expression is,
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
Related Questions to study
Use polynomial identities to factor each polynomial : ![open parentheses 8 x to the power of 6 minus y cubed close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAATCAYAAADcZiBNAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAnpJREFUeNrdWNFHZFEcHkmSREZW9mHJPqxkxDysJIm1kjWyJEkylpWVNf/A2odEkh6yb2sfkkRWDyuJJEkSyVrZh6GHtQ9Z0cPKGtfSfj++yek350wzc+feO/bj495z5p753e/8zvc758Zi4eMpuA/mwBsybOT/1wO/gs9jNYRO8BTsqqGYnoA/ynngDTgXYEDLYF+stlAHXhn3c9TBigR4FHBAl+A4Zy4LjkQsUBz8AKZV+yH1KIB0dKu2JnAJvKaHbIMPfQT1F/wItoANvE5HJFDelyYsfUnwQDd2UySNT+AsWM+XklQ89hFYlumdR3O5flBltPD9Xlv6DijWLebBacsPc5b16/kISjKn1bgX4U9qwJdylra32p+3HYZ6zdk2Rfpp+d0rh+HPsM/0vWXOYD39YLDKLyzZP2ppzzBrNPocE9UD7poNvzmrGktU1HxwwRGclPYHxn2aImiIcZ+DvwIy7kmuDO2tWRq16Ud5n31kGaeButwxVFfF80jZAF4UKeGSEYu8fqZnIUQMgeuq7T34roKxvPtEEnVXwXYjy5LMgoRj0B2wn7vYeJWqTzG6yvqZcd/GmBv9imRbbhsOMQbAPcegGQ6ciNiI/xjXi4yrXBQsN8mA3hIcv1ifPP+ZQY1FLJKU7w7yXG07SkWBcdu2AN/Bx47z14Vqk2C+0CCbWS3iEYokFTRFu5iocIxpXQBsm8mXFGqAM1HHa5mZKbXmt5QoL8CVCEXKcCvwzWc2JnXjkcVLRljaPS4xqXDDat1uOI4qawHsgUrFMI09VeHz1mNJWAfcsJDy+S6HxYrPVMCfSsLCFo23Esw7znL/FeSD3mY1B/wHt1GNt7iJMnUAAADLdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1yb3c+PG1uPjg8L21uPjxtc3VwPjxtaT54PC9taT48bW4+NjwvbW4+PC9tc3VwPjxtbz4mI3gyMjEyOzwvbW8+PG1zdXA+PG1pPnk8L21pPjxtbj4zPC9tbj48L21zdXA+PC9tcm93PjwvbWZlbmNlZD48L21hdGg+i9T4lAAAAABJRU5ErkJggg==)
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 factor each polynomial : ![open parentheses 8 x to the power of 6 minus y cubed 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 factor each polynomial : ![open parentheses 36 a squared minus 4 b squared close parentheses](data:image/png;base64,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)
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions
Use polynomial identities to factor each polynomial : ![open parentheses 36 a squared minus 4 b squared close parentheses](data:image/png;base64,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)
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions
Use polynomial identities to multiply each expression ![open parentheses x plus 3 y cubed close parentheses squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAWCAYAAACMq7H+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAATRJrTQAAAAkVJREFUeNrtWN9HQ1Ecn2SSRCaTHmKSHpLRUzKJJMkkkh6SiSRJ/0B6SMwepodee0gSSQ/JRJLMTCSTHhJJ/0APPcw1Ud9vPuN2nLPdc+/uZj8+fNg959x7zvmc768zj6eBPH7AHDFF7G1IokYTcY342JCiOIx6cp0McULz/VHiXT1ZRD/xQ2N8F2JSQDWAfTFagzHm0/QcxT5l6CNeQigpBonpGhPIR9wnRoT2FPYrWlCC2F7og/xisIIbGsMiswiar8Q9bNRJXFqU9A0Rk0JbAq6pRBAiVRK3xFmiV1jXlYNvslXsElckfUmIJYpq5j/EiOsuZhon+HIpnW/oxl8+rZCkfVnxoR30uS0SZ5gXoe2AOC8ZuwmrEcH7epC0DxNvdE/Lq+jjytNveo4gGLppSX7Mw3FpSuhbguWb0YqxPsF1DBhAj2QOr66VfhfomyTG8XtcV31NkcSYsCkZw6KdCm3bxC0bh5ErlUiMa1ShGQvZ5scCi6GDOEO8x7xiWn82PXcS34gtbotUyN3y/p6T1BZux6Q2CCUia/odV1hcMWi7G1vKiKKP28+wmIUKZDdDkb4D4Buqal1oB25VCcCLuEBgbEOW8JVRpEEEZBGHxDDxWFEsWsG6JAF4dIvJTlShZlGmiUcuicS37jliMyyDK/B3ZDOZ+3Mp8OTgAMRi0hLSppjD/npO7JaMO0HGKzVCuFwa4C0ORYYZiB+2OZfsWmLZtKvlght2uNaUzST0h9Uq+askgcBrBzHFXa6mMAC3LBt+Aed/jJA6W/NFAAAAxHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3VwPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93PjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjM8L21uPjxtc3VwPjxtaT55PC9taT48bW4+MzwvbW4+PC9tc3VwPjwvbXJvdz48L21mZW5jZWQ+PG1uPjI8L21uPjwvbXN1cD48L21hdGg+a23gxwAAAABJRU5ErkJggg==)
Any expression of the form (a + b)2 can be expanded using the identity rather than using the conventional and time taking method of multiplying them, (a + b)(a + b)
Use polynomial identities to multiply each expression ![open parentheses x plus 3 y cubed close parentheses squared](data:image/png;base64,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)
Any expression of the form (a + b)2 can be expanded using the identity rather than using the conventional and time taking method of multiplying them, (a + b)(a + b)
Use polynomial identities to factor the polynomials or simplify the expressions :
![8 cubed minus 2 cubed](data:image/png;base64,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)
Use polynomial identities to factor the polynomials or simplify the expressions :
![8 cubed minus 2 cubed](data:image/png;base64,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)
Dakota said the third term of the expansions of
is .Explain Dakota’s error and then correct the answer.
Dakota said the third term of the expansions of
is .Explain Dakota’s error and then correct the answer.
Use polynomial identities to multiply each expression .![left parenthesis 2 x plus 8 y right parenthesis left parenthesis 2 x minus 8 y right parenthesis](data:image/png;base64,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)
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
Use polynomial identities to multiply each expression .![left parenthesis 2 x plus 8 y right parenthesis left parenthesis 2 x minus 8 y right parenthesis](data:image/png;base64,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)
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
What number does C3 represent in the expansion
? Explain.
What number does C3 represent in the expansion
? Explain.
Dakota said the third term of the expansions of
.Explain Dakota’s error and then correct the answer.
You can use Both the Pascal’s triangle and binomial expansion to find the value of (x + y)n .
Dakota said the third term of the expansions of
.Explain Dakota’s error and then correct the answer.
You can use Both the Pascal’s triangle and binomial expansion to find the value of (x + y)n .
What number does C3 represent in the expansion
? Explain.
The value is called the combination permutation.
What number does C3 represent in the expansion
? Explain.
The value is called the combination permutation.
Explain how to use a polynomial identity to factor .![8 x to the power of 6 minus 27 y cubed](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFMAAAATCAYAAADs6jFsAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAoFJREFUeNrtl99HpFEcxsdIkgwZSbqIdJFkRBdJsmKtJMkykmSNJV1l/oF0kUgyF6u77EVWIkmSEVlJkkiStdbQxeoiib1YyWtEPYfn5TjOeefMvDNvNebhw/vjzJzzfs/3PN9zQqHSqgccAQc8k/cu9zuy4BJ8CqLTDnABOkPlq3bwN4iO1kB/qLwVBv+C6OgeTHDmMiBeZoGMghWQ0L2sBd/AAz1uHzT76OwJrIIIqOZ1osgf1Ae2wH/JwyY8fM5Eob45aWrwHSyAKn78Ijjz8aEZLgNXdSXwF1Hcxvnfrk+f8JmN4pzkQhRhvKZ0Lx2NH2R9fKgYZL10LyboPIDl1wKuLNo1gmNQ47M/R/fwQZphN5g3mnZfmbWq5vnOVYxFKMJsF/4yGJCfORZtdkGXZnWOadommYWq+k0JIvxyRrrvBcuGgVxwZl0lGCxVwr+uwV2ABaiXS91L02BW8/wLWNLUkgwLjuyXbl1p0XUQ47LO0otuPbY2IsNSvP4Ifr6RCltDn+/LYQNnXC2qhsCm8mzOEHjPDtZBE71NqJtZFTP85gB8YAWNFulU4afiCn/esTiRiEQZ8Nju/JLuGxiDvHx12xA00emh4TdJZnHsDWRkKwPZZlG90znaPErXKX5n0Qzb8djfpfLYhpTySLdKb8t1WvmjKTqqjjk5rczKcL4D+m2Y1Q56p5oFuxx8HatZ9JUC2UiPq7JoO8olbnMMHqHtTRYyqM8M6ABnIszra1Y+2UPSSvCGwY9XCuYeM9NGG5YnsCS3SFd+BhbnlifLpX3E2ZQ33duGI+ZGgHtI28Kl6k45RHhl8DOzsyKfEkE8rYShOEpz41+RT3XShwvSC5tDl2bIseHYAAAAp3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbj44PC9tbj48bXN1cD48bWk+eDwvbWk+PG1uPjY8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtbj4yNzwvbW4+PG1zdXA+PG1pPnk8L21pPjxtbj4zPC9tbj48L21zdXA+PC9tYXRoPlXdeccAAAAASUVORK5CYII=)
Explain how to use a polynomial identity to factor .![8 x to the power of 6 minus 27 y cubed](data:image/png;base64,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)
Use polynomial identities to factor the polynomials or simplify the expressions :
![10 cubed minus 3 cubed](data:image/png;base64,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)
Use polynomial identities to factor the polynomials or simplify the expressions :
![10 cubed minus 3 cubed](data:image/png;base64,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)
How are Pascal’s triangle and binomial expansion such as
related?
How are Pascal’s triangle and binomial expansion such as
related?
Explain how to use a polynomial identity to factor
.
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.
Explain how to use a polynomial identity to factor
.
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.