Answer:
[tex]x^4 - 81 = (x - 3)(x+3)(x^2 + 9)[/tex]
Step-by-step explanation:
Given
[tex]x^4 - 81[/tex]
Required
Write an equivalent expression
Express 81 as 9^2
[tex]x^4 - 81 = x^4 - 9^2[/tex]
Express x^4 as (x^2)^2
[tex]x^4 - 81 = (x^2)^2 - 9^2[/tex]
Apply difference of two squares:
[tex]x^4 - 81 = (x^2 - 9)(x^2 + 9)[/tex]
Express 9 as 3^2
[tex]x^4 - 81 = (x^2 - 3^2)(x^2 + 9)[/tex]
Apply difference of two squares
[tex]x^4 - 81 = (x - 3)(x+3)(x^2 + 9)[/tex]
Hence, an equivalent expression is: [tex](x - 3)(x+3)(x^2 + 9)[/tex]
