Question

Eli needs to place buoys at specific points in the inlet. He used the expression x4−81 to find the location for each buoy. Which expression is equivalent to Eli's expression?

Answer 1

`x^4 - 81 = (x - 3)(x+3)(x^2 + 9)`

Explanation:

Given

`x^4 - 81`

Required

Write an equivalent expression

Express 81 as 9^2

`x^4 - 81 = x^4 - 9^2`

Express x^4 as (x^2)^2

`x^4 - 81 = (x^2)^2 - 9^2`

Apply difference of two squares:

`x^4 - 81 = (x^2 - 9)(x^2 + 9)`

Express 9 as 3^2

`x^4 - 81 = (x^2 - 3^2)(x^2 + 9)`

Apply difference of two squares

`x^4 - 81 = (x - 3)(x+3)(x^2 + 9)`

Hence, an equivalent expression is:
`(x - 3)(x+3)(x^2 + 9)`