Maths-
General
Easy

Question

How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 123 + 23

hintHint:

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 values, 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: = 1736



    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 with the help of identities, which would speed up the process and make it simple.
    Here, the given expression is 123 + 23 where a=12 and b=2
    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:
    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 12 cubed plus 2 cubed equals left parenthesis 12 plus 2 right parenthesis open parentheses 12 squared minus 12 left parenthesis 2 right parenthesis plus 2 squared close parentheses end cell row cell equals 14 left parenthesis 144 minus 24 plus 4 right parenthesis end cell row cell equals 14 left parenthesis 124 right parenthesis end cell row cell equals 1736 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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