Maths-
General
Easy

Question

Use polynomial identities to factor the polynomials or simplify the expressions : x9 - 8

hintHint:

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 , here a and b can be real values, variables or multiples of both. We are asked to use polynomial identities to factorize the given expression.

The correct answer is: x9 - 8 = (x3 - 2)(x6 + 2x3 + 4)


     Step 1 of 2:
    The given expression is x9 - 8 . We can rewrite it as, x to the power of 9 minus 8 equals open parentheses x cubed close parentheses cubed minus left parenthesis 2 right parenthesis cubed . It is of the form open parentheses a cubed minus b cubed close parentheses . Here, a equals x cubed straight & b equals 2 .
    Step 2 of 2:
    Use the polynomial identity to simplify 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 x to the power of 9 minus 8 equals open parentheses x cubed close parentheses cubed minus left parenthesis 2 right parenthesis cubed end cell row cell equals open parentheses x cubed minus 2 close parentheses open parentheses open parentheses x cubed close parentheses squared plus open parentheses x cubed close parentheses left parenthesis 2 right parenthesis plus open parentheses 2 squared close parentheses close parentheses end cell row cell equals open parentheses x cubed minus 2 close parentheses open parentheses x to the power of 6 plus 2 x cubed plus 4 close parentheses end cell end table
    Thus, the simplified expression is; x to the power of 9 minus 8 equals open parentheses x cubed minus 2 close parentheses open parentheses x to the power of 6 plus 2 x cubed plus 4 close parentheses.
     

    Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions

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