Question

Refer to the rectangle below. The length of the rectangle is x + 12. The width of the rectangle is x + 3.

Answer 1

Answer:

$x^2+15x+36$

Step-by-step explanation:

The complete question is shown in the attachment.

The length of the rectangle is x + 12. The width of the rectangle is x + 3.

Recall that area of a rectangle is $Length \times Width$

In terms of x, the area is $(x+12)(x+3)$

Recall the distributive property of real numbers: $(a+b)(c+d)=a(c+d)+b(c+d)$

We apply this property to get:

$(x+12)(x+3)=x(x+3)+12(x+3)$

We expand again to get:

$(x+12)(x+3)=x^2+3x+12x+36$

We now simplify to obtain:

$(x+12)(x+3)=x^2+15x+36$

The area of the rectangle is $x^2+15x+36$