Question

Which expressions are equivalent to (2^2-9) (x + 3)?

Select the THREE equivalent expressions.
A) (x+3)^2 (x – 3)
B) (0 - 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`