What is [tex]x^4 - 81[/tex] factored?

x 4 − 81 = ( x 2 ) 2 − 9 2 = ( x 2 − 9 ) ( x 2 + 9 ) = ( x 2 − 3 2 ) ( x 2 + 9 ) = = ( x − 3 ) ( x + 3 ) ( x 2 + 9 )

Answered by kate200468 | 2024-06-10

What we need here:
"The difference of two squares is the same as (their sum) times (their difference)."
x^4 is the square of x² . 81 is the square of 9 . Their difference is the same as (x² + 9) times (x² - 9).
But (x² - 9) is also the difference of two squares, so it's the same thing as (x+ 3) times (x-3).
So the complete factored form of the original expression is
(x^4 - 81) = (x² + 9) (x+3) (x - 3)

Answered by AL2006 | 2024-06-25

The expression x 4 − 81 can be factored as ( x − 3 ) ( x + 3 ) ( x 2 + 9 ) . This follows from recognizing it as a difference of squares, which is a standard algebraic technique. The first step is to split it into ( x 2 − 9 ) ( x 2 + 9 ) , and then factor x 2 − 9 further into ( x − 3 ) ( x + 3 ) .
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Answered by kate200468 | 2024-10-08