Question

1. For each expression, write an equivalent expression in standard formby using the distributive property. Show your reasoning.a. (2x + 5)(x + 1)b. (x - 2)(x + 2)

Answer 1

Given the following equation,

a. (2x + 5)(x + 1)

b. (x - 2)(x + 2)

Let's transform them into an equivalent standard form using the distributive property:

$\text{ Standard Form: Ax}^2\text{ + Bx + C}$

We get,

a. (2x + 5)(x + 1)

(2x + 5)(x + 1) = (2x)(x) + (2x)(1) + (5)(x) + (5)(1)

= 2x² + 2x + 5x + 5

(2x + 5)(x + 1) = 2x² + 7x + 5

b. (x - 2)(x + 2)

(x - 2)(x + 2) = (x)(x) + (x)(2) + (-2)(x) + (-2)(2)

= x² + 2x - 2x - 4

(x - 2)(x + 2) = x² - 4