Maths-
General
Easy

Question

How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 27 x to the power of 9 minus 343 y to the power of 6

Hint:

open parentheses a cubed minus b cubed close parentheses equals left parenthesis a minus b right parenthesis open parentheses a squared plus 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: = (3x3 - 7y2)(9x6 + 21x3y2+49y4)


    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 27 x to the power of 9 minus 343 y to the power of 6. This can be written as: open parentheses 3 x cubed close parentheses cubed minus open parentheses 7 y squared close parentheses cubed where a equals 3 x cubed straight & b equals 7 y squared .
    Step 2 of 2:
    Substitute the values in the expression open parentheses a cubed minus b cubed close parentheses equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses for factorization:

    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 3 x cubed close parentheses cubed minus open parentheses 7 y squared close parentheses cubed equals open parentheses 3 x cubed minus 7 y squared close parentheses open parentheses open parentheses 3 x cubed close parentheses squared plus open parentheses 3 x cubed close parentheses open parentheses 7 y squared close parentheses plus open parentheses 7 y squared close parentheses squared close parentheses end cell row cell equals open parentheses 3 x cubed minus 7 y squared close parentheses open parentheses 9 x to the power of 6 plus 21 x cubed y squared plus 49 y to the power of 4 close parentheses end cell end table
     

    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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