Maths-
General
Easy

Question

Use polynomial identities to multiply the expressions ?
18 × 22

The correct answer is: Thus, the product is: 18 × 22 = 396


    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 18 × 2.text  It can be written as  end text left parenthesis 20 minus 2 right parenthesis cross times left parenthesis 20 plus 2 right parenthesis text . This 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 20 straight & b equals 2 text .  end text
    Step 2 of 2:
    Use the identity open parentheses a squared minus b squared close parentheses equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesisto 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 18 cross times 22 equals left parenthesis 20 minus 2 right parenthesis cross times left parenthesis 20 plus 2 right parenthesis end cell row cell equals 20 squared minus 2 squared space space space space space space space space space space space space space space space space space space end cell row cell equals 400 minus 4 space space space space space space space space space space space space space space space space space space space end cell row cell equals 396 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: 18 × 22 = 396
    Note:
    Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.

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