Maths-
General
Easy

Question

Use polynomial identities to multiply the expressions ?
open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses

The correct answer is: Thus, the product is (3x^2-4xy)(3x^2 + 4xy) = 9x^4-16x^2 y^2.


    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 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y 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 3 x squared straight & b equals 4 x y
    Step 2 of 2:
    Use the polynomial identity to find the product of 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 open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses equals open parentheses 3 x squared close parentheses squared minus left parenthesis 4 x y right parenthesis to the power of 2 space space space space space space space end exponent end cell row cell equals 9 x to the power of 4 minus 16 x squared y squared 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
    Thus, the product is open parentheses 3 straight x squared minus 4 xy close parentheses open parentheses 3 straight x squared plus 4 xy close parentheses equals 9 straight x to the power of 4 minus 16 straight x squared straight y squared.
    Note:
    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.

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