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Easy

Question

Use polynomial identities to factor the polynomials or simplify the expressions : x cubed minus 27 y cubed

hintHint:

open parentheses a cubed minus b cubed close parentheses equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses , 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.

The correct answer is: x3 - 27y3 = (x - 3y)(x2 + 3xy + 9y2)


     Step 1 of 2:
    The given expression is x cubed minus 27 y cubed . It can be written as left parenthesis x right parenthesis cubed minus left parenthesis 3 y right parenthesis cubed . It is of the form a cubed minus b cubed where a equals x straight & b equals 3 y .
    Step 2 of 2:
    Use polynomial identities to simplify the given 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 x cubed minus 27 y cubed equals left parenthesis x right parenthesis cubed minus left parenthesis 3 y right parenthesis cubed end cell row cell equals left parenthesis x minus 3 y right parenthesis open parentheses x squared plus left parenthesis x right parenthesis left parenthesis 3 y right parenthesis plus left parenthesis 3 y right parenthesis squared close parentheses end cell row cell equals left parenthesis x minus 3 y right parenthesis open parentheses x squared plus 3 x y plus 9 y squared close parentheses end cell end table
    The factor of the expression is x cubed minus 27 y cubed equals left parenthesis x minus 3 y right parenthesis open parentheses x squared plus 3 x y plus 9 y squared close parentheses

    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants

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