Maths-
General
Easy

Question

Use polynomial identities to multiply the expressions ?
open parentheses x squared plus y to the power of 6 close parentheses squared

The correct answer is: Thus, the product is


    ANSWER:
    Hint:
    left parenthesis x plus a right parenthesis squared equals x squared plus 2 a x plus a squared, where a and x 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:
    text  The given expression is  end text open parentheses x squared plus y to the power of 6 close parentheses squared text . It is of the form  end text left parenthesis x plus a right parenthesis squared text  where  end text x equals x squared straight & a equals y to the power of 6 text .  end text
    Step 2 of 2:
    Use the identity  left parenthesis straight x plus straight a right parenthesis squared equals straight x squared plus 2 ax plus straight a squared 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 x squared plus y to the power of 6 close parentheses squared equals open parentheses x squared close parentheses squared plus 2 open parentheses x squared close parentheses open parentheses y to the power of 6 close parentheses plus open parentheses y to the power of 6 close parentheses squared end cell row cell equals x to the power of 4 plus 2 x squared y to the power of 6 plus y to the power of 12 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
    text  Thus, the product is:  end text open parentheses x squared plus y to the power of 6 close parentheses squared equals x to the power of 4 plus 2 x squared y to the power of 6 plus y to the power of 12
    Note:
    We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.

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