Maths-
General
Easy

Question

Use polynomial identities to multiply the expressions ?
open parentheses 4 straight x squared plus 6 straight y squared close parentheses open parentheses 4 straight x squared minus 6 straight y squared close parentheses

The correct answer is: Hence, the product is


    ANSWER:
    Hint:
    open parentheses a squared minus b squared close parentheses equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis, where a and b can be real values, variables or multiples of both.
    We are asked to use polynomial identities to find the product of the expression.
    Step 1 of 2:
    The given expression is open parentheses 4 x squared plus 6 y squared close parentheses open parentheses 4 x squared minus 6 y squared close parentheses text . It is of the form  end text left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis text  where  end text a equals 4 x squared straight & b equals 6 y squared text .  end text
    Step 2 of 2:
    Use the identity  a equals 4 x squared straight & b equals 6 y squaredto find the product. Thus, we have:
    table attributes columnalign right columnspacing 0em end attributes row cell open parentheses 4 straight x squared plus 6 straight y squared close parentheses open parentheses 4 straight x squared minus 6 straight y squared close parentheses equals open parentheses 4 straight x squared close parentheses squared minus open parentheses 6 straight y squared close parentheses squared end cell row cell equals 16 straight x to the power of 4 minus 36 straight y to the power of 4 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
    text  Hence, the product is  end text open parentheses 4 x squared plus 6 y squared close parentheses open parentheses 4 x squared minus 6 y squared close parentheses equals 16 x to the power of 4 minus 36 y to the power of 4
    Note:
    Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.

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