Maths-
General
Easy

Question

How can you use polynomial identities to factor polynomials and simplify numerical expressions ? open parentheses 11 cubed close parentheses plus 5 cubed

Hint:

open parentheses a cubed plus b cubed close parentheses equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses , where a and b can be real numbers, variables or multiples of both. We are asked to explain on how the polynomial identities can be used to factorize polynomials and simplify them.

The correct answer is: = 1456


    Step 1 of 2:
    Factoring a polynomial is the process of decomposing a polynomial into a product of two or more polynomials. This can be done using identities, which would speed up the process and make it simple.
    Here, the given expression is open parentheses 11 cubed close parentheses plus 5 cubed where a equals 11 straight & b equals 5
    Step 2 of 2:
    Now, substitute the values in the identity open parentheses a cubed plus b cubed close parentheses equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses to factorize them.

    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 11 cubed close parentheses plus 5 cubed equals left parenthesis 11 plus 5 right parenthesis open parentheses 11 squared minus 11 left parenthesis 5 right parenthesis plus 5 squared close parentheses end cell row cell equals left parenthesis 16 right parenthesis left parenthesis 121 minus 55 plus 25 right parenthesis end cell row cell equals 16 left parenthesis 91 right parenthesis end cell row cell equals 1456 end cell end table
     

    This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.

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