Question

Find the area of the shaded region

Answer 1

Answer:

$\mathsf{ {5x}^{2} + 28x + 21}$

Option A is the right option.

Step-by-step explanation:

Let's find the area of large rectangle:

$\mathsf{(3x + 6)(2x + 4)}$

Multiply each term in the first parentheses by each term in the second parentheses

$\mathsf{ = 3x(2x + 4) + 6(2x + 4)}$

Calculate the product

$\mathsf{ = 6 {x}^{2} + 12x + 12x + 6 \times 4}$

Multiply the numbers

$\mathsf{ = 6 {x}^{2} + 12x + 12x + 24}$

Collect like terms

$\mathsf{ = {6x}^{2} + 24x + 24}$

Let's find the area of small rectangle

$\mathsf{(x - 3)(x - 1)}$

Multiply each term in the first parentheses by each term in the second parentheses

$\mathsf{ = x( x - 1) - 3(x - 1)}$

Calculate the product

$\mathsf{ = {x}^{2} - x - 3x - 3 \times ( - 1)}$

Multiply the numbers

$\mathsf{ = {x}^{2} - x - 3x + 3}$

Collect like terms

$\mathsf{ = {x}^{2} - 4x + 3}$

Now, let's find the area of shaded region:

Area of large rectangle - Area of smaller rectangle

$\mathsf{6 {x}^{2} + 24x + 24 - ( {x}^{2} - 4x + 3)}$

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

$\mathsf{ = {6x}^{2} + 24x + 24 - {x}^{2} + 4x - 3}$

Collect like terms

$\mathsf{ = {5x}^{2} + 28x + 21}$

Hope I helped!

Best regards!