Maths-
General
Easy

Question

Use polynomial identities to factor each polynomial : open parentheses 36 a squared minus 4 b squared close parentheses

hintHint:

left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis equals open parentheses a squared minus 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 factorize each expression.

The correct answer is: (6a - 2b)(6a + 2b)


    Step 1 of 2:
    The given expression is open parentheses 36 a squared minus 4 b squared close parentheses . It can be written as: left parenthesis 6 a right parenthesis squared minus left parenthesis 2 b right parenthesis squared . It is of the form open parentheses a squared minus b squared close parentheses where a equals 6 a straight & b equals 2 b .
    Step 2 of 2:
    Substitute the values in the expansion to get the factor form. Thus, we have:

    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 36 a squared minus 4 b squared close parentheses equals left parenthesis 6 a right parenthesis squared minus left parenthesis 2 b right parenthesis squared end cell row cell equals left parenthesis 6 a minus 2 b right parenthesis left parenthesis 6 a plus 2 b right parenthesis end cell end table
    Hence, the factor is, open parentheses 36 a squared minus 4 b squared close parentheses equals left parenthesis 6 a minus 2 b right parenthesis left parenthesis 6 a plus 2 b right parenthesis .

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

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