The problem asks us to choose the THREE expressions that are equivalent to the factorization $(2x + 3)(2x - 5)$.

1. Problem Description

The problem asks us to choose the THREE expressions that are equivalent to the factorization $(2x + 3)(2x - 5)$.

2. Solution Steps

First, expand the expression $(2x + 3)(2x - 5)$:

$(2x + 3)(2x - 5) = 2x(2x - 5) + 3(2x - 5) = 4x^2 - 10x + 6x - 15 = 4x^2 - 4x - 15$.

Now, we need to check each of the five given expressions to see if they are equivalent to $4x^2 - 4x - 15$.

a) $4x^2 + 6x - 5(2x + 3) = 4x^2 + 6x - 10x - 15 = 4x^2 - 4x - 15$.

This expression is equivalent to $(2x + 3)(2x - 5)$.

b) $4x^2 - 10x + 3(2x - 5) = 4x^2 - 10x + 6x - 15 = 4x^2 - 4x - 15$.

This expression is equivalent to $(2x + 3)(2x - 5)$.

c) $4x^2 + 6x + 5(2x + 3) = 4x^2 + 6x + 10x + 15 = 4x^2 + 16x + 15$.

This expression is not equivalent to $(2x + 3)(2x - 5)$.

d) $2x(2x + 3) - 5(2x - 3) = 4x^2 + 6x - 10x + 15 = 4x^2 - 4x + 15$.

This expression is not equivalent to $(2x + 3)(2x - 5)$.

e) $2x(2x + 3) - 10x - 15 = 4x^2 + 6x - 10x - 15 = 4x^2 - 4x - 15$.

This expression is equivalent to $(2x + 3)(2x - 5)$.

3. Final Answer

The three expressions that result in the factorization $(2x + 3)(2x - 5)$ are:

$4x^2 + 6x - 5(2x + 3)$

$4x^2 - 10x + 3(2x - 5)$

$2x(2x+3) - 10x - 15$