Question
Use polynomial identities to factor the polynomials or simplify the expressions :
![8 cubed minus 2 cubed](data:image/png;base64,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)
The correct answer is: Thus, the answer is; 8^3 - 2^3 = 504
ANSWER:
Hint:
, here a and b can be real values, variables or multiples of both.
We are asked to use polynomial identities to factorize the given expression.
Step 1 of 2:
The given expression is ![8 cubed minus 2 cubed text . It is of the form end text open parentheses a cubed minus b cubed close parentheses text where end text a equals 8 straight & b equals 2 text . end text](data:image/png;base64,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)
Step 2 of 2:
Use polynomial identities 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 8 cubed minus 2 cubed equals left parenthesis 8 minus 2 right parenthesis open parentheses 8 squared plus left parenthesis 8 right parenthesis left parenthesis 2 right parenthesis plus 2 squared close parentheses end cell row cell equals 6 left parenthesis 64 plus 16 plus 4 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell row cell equals 6 left parenthesis 84 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell row cell equals 504 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell end table](data:image/png;base64,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)
Thus, the answer is;![8 cubed minus 2 cubed equals 504](data:image/png;base64,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)
Note:
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.
Related Questions to study
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,iVBORw0KGgoAAAANSUhEUgAAAIYAAAARCAYAAAAYGtRqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAApZJREFUeNrtWd9HZFEcP0bGSC/JyuphSQ/JGtFTshJrJRmJtUbWWkuykv6BtQ+JZM1DeksPSSLJWsmyxlojWdZaa+3D0lMPvWesMaI+5/oMp9M53TO3bo6Z++HDPfeee+acz3x/nXOFuIq34JJoDixxvTYkWhBZ8Eg0Fw657kQLuxbBg36lPQTugmdgFfwFTnmyiFZwBSyDFfAz2BVhnAGwlGhh16KfYqj4BubBNrb72CfvgRjr4CLYAqYZCr9HHKtEURItrmshlsFZhxcfgb9jWuBFHX0rWjtFT46COa2W8EEL4YkWQfh5EnEiEm8shdoCn921YZQV762JcWLwpBeGd+fpYTUMgkXPtBCeaBHkzrTDJAYNYbaGn2Cn0n4NrsYUMVZo3eq8Pmh9XtH79Xz8D+xQ7qW5fp+0EJ5oIc4dJpBh7hqyPB8FC7x+qlveHRtGluGyyvx/avDyMXBHu/cefGcYr+qZFsITLULFaAc/gs9C+n0Bh1m1dzgYQhhtuX0LfKh4tiyYjrXtlvz9P0r7AftkbmkYzaTFjeGzm0L0OFjvPAfOxlh87lnGHwG/avf+K9cFzk9HPankvrQQnmgRWLcpLPaCa8xHYajt9QsRt3GuhlGp41mJf2Y3PSRlqRWKnmkhPNHCuEXrZF5qcZig/LFPFE1WyD8cwmdUw/hr8dg+5lcVG2CO4falZbxZrTDzQQvhiRbGQ519ekkYZL460BY/Dm7GZBiTFGSEVp/itfSCGUM4Xw85b3A54LpvLYQnWgQ40vKVSyGUZp4zHcFuszqPA8+5JawyZMpqfMLQb4LzzVnGsR2JJ1po255G+3CUC1lTM31Ei6pFgBnRWJ+aD1hQmSBz6fQN7yZaNCgeszZIEEGLS82gB8pDtNW+AAAA0nRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4oPC9tbz48bW4+MjwvbW4+PG1pPng8L21pPjxtbz4rPC9tbz48bW4+ODwvbW4+PG1pPnk8L21pPjxtbz4pPC9tbz48bW8+KDwvbW8+PG1uPjI8L21uPjxtaT54PC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj44PC9tbj48bWk+eTwvbWk+PG1vPik8L21vPjwvbWF0aD6p0GMZAAAAAElFTkSuQmCC)
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,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)
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,iVBORw0KGgoAAAANSUhEUgAAAD8AAAARCAYAAABq+XSZAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAXBJREFUeNpjYKAN+A/Fv4D4AhC7MQwcGFC3aADxQ4bBAejuFiYgfjdIPE9XtwgD8RQgThwEHifoFjUgroXmDVyAD4inAfFJKJ4JFcOV12Jp5BlHIN4GxN+A+AcQ3wLiCVBPkuWWxUCcBlWIC+wFYj8kvg9UDFdAtULNpDbYD8RBQMyGJGYAxDsodQsuz4cC8SQs4qAQj8Rj3g86Ju9PBOR/kOv5NTiqCkeoHDZgC8Rn6ORxJSC+gUeeKLfg8vw7tGQGAyCxl1jy2A9oMpSnsafFoQUZKN974cjvRLsFl+f/4NHzawAbMDBcQC1DSfX8Dyp5ABsmBASBOABa+9jTyvMvcSR7DrRkP1CABxoANPE8qFDzwCLuhqfAozf4QSvPg+rV2VjE5xOo6ugF9KCFHk08D2tcgAoWFmgWqAbigwPg0YPQdgcLtM0Oqm7vA3E8AxULH2yFy1xo8voGbd7yDIDnQXX2Fqg7fkAjxYdhFBAHADADba9Tb0OXAAAAk3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3VwPjxtbj4xMDwvbW4+PG1uPjM8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtc3VwPjxtbj4zPC9tbj48bW4+MzwvbW4+PC9tc3VwPjwvbWF0aD7v3q5xAAAAAElFTkSuQmCC)
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.