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Easy

Question

Use polynomial identities to factor each polynomial : m to the power of 9 plus 27 n to the power of 6

hintHint:

a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses 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 m to the power of 9 plus 27 n to the power of 6 . It can be written as open parentheses m cubed close parentheses cubed plus open parentheses 3 n squared close parentheses cubed . This is of the form a cubed plus b cubed where a equals m cubed straight & b equals 3 n squared .
    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
    The factor of the expression is, m to the power of 9 plus 27 n to the power of 6 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 .

    Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.

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