Maths-
General
Easy

Question

Use polynomial identities to multiply the expressions ?
103 × 97

The correct answer is: Thus, the product is 103 × 97 = 9991


    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 103 cross times 97 text . It can be written as  end text 103 cross times 97 equals left parenthesis 100 plus 3 right parenthesis left parenthesis 100 minus 3 right parenthesis text .  end text
    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 100 straight & b equals 3 text .  end text
    Step 2 of 2:
    Applying the identity on the expression, we get:
    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 103 cross times 97 equals left parenthesis 100 plus 3 right parenthesis left parenthesis 100 minus 3 right parenthesis end cell row cell equals 100 squared minus 3 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 end cell row cell equals 10 comma 000 minus 9 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 row cell equals 9991 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  103 × 97 = 9991
    Note:
    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.

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