Question

Which expressions are equivalent to (x²- 9) (x+3)?

Select the three equivalent expressions.
A) (x+3)² (x-3)
B) (x-3)² (x+3)
C) (x+3)³
D) (x+3) (x+3) (x-3)
E) (x+3) (x-3) (x-3)
F) [(x)²+ (3)²] (x-3)

Answer 1

`(x^2-3^2)(x+3)`

`(x-3)(x+3)(x+3)`

`(x-3)(x+3)^2`

Explanation:

Given

`(x^2-9)(x+3)`

Required

Select 3 equivalent expressions

`(x^2-9)(x+3)`

Express 9 as 3^2

`(x^2-3^2)(x+3)` --- This is one equivalent expression

Take
`x^2 - 3^2` as difference of two squares

`(x-3)(x+3)(x+3)` -- This is another equivalent expression:

Solving further:

`(x-3)(x+3)(x+3)` becomes

`(x-3)(x+3)^2` -- This is another equivalent expression:

Hence, the equivalent expressions are:

`(x^2-3^2)(x+3)`

`(x-3)(x+3)(x+3)`

`(x-3)(x+3)^2`