Maths-
General
Easy

Question

Use polynomial identities to multiply the expressions ?
left parenthesis 2 x minus 5 right parenthesis left parenthesis 2 x plus 5 right parenthesis

The correct answer is: There are some basic polynomial identities that you need to by heart.


    ANSWER:
    Hint:
    open parentheses straight a squared minus straight b squared close parentheses equals left parenthesis straight a minus straight b right parenthesis left parenthesis straight a plus straight 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:
    text  The given expression is  end text left parenthesis 2 x minus 5 right parenthesis left parenthesis 2 x plus 5 right parenthesis 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 2 x straight & b equals 5
    Step 2 of 2:
    Use the polynomial identity open parentheses a squared minus b squared close parentheses equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis to find the product of the given 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 left parenthesis 2 x minus 5 right parenthesis left parenthesis 2 x plus 5 right parenthesis equals left parenthesis 2 x right parenthesis squared minus 5 squared end cell row cell equals 4 x squared minus 25 end cell end table
    text  Thus, the product is  end text left parenthesis 2 x minus 5 right parenthesis left parenthesis 2 x plus 5 right parenthesis equals 4 x squared minus 25
    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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