Question

Wite an expression in simplest form to represent the area of the shaded region

Answer 1

Distribute the 4x to the 3x+2 to get 12x^2+8x

Multiply 2x and 3x to get 6x^2

then combine like terms to get your final answer of 6x^2+8x

Answer 2

The expression in simplest form which represent the area of the shaded region is,

$6x^2+8x$

What is area of rectangle?

Area of rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

$A=a\times b$

Here, $a$is the length rectangle and $b$ is the width of the rectangle.

Given information-

The length of the inner rectangle is 2x.

The width of the inner rectangle is 3x.

The length of the outer rectangle is 3x+2.

The width of the outer rectangle is 4x.

As the area of the rectangle is the product of the length of the rectangle and the width of the rectangle. Thus, the area of inner rectangle is,

$A_i=2x\times3x\\A_i=6x^2$

The area of outer rectangle is,

$A_o=4x\times(3x+2)\\A_o=12x^2+8x$

The area of the shaded region is the difference of area of outer rectangle and the area of inner rectangle. Thus the area of the shaded region is,

$A=A_o-A_i$

Put the values as,

$A=12x^2+8x-6x^2\\A=6x^2+8x$

Hence, The expression in simplest form which represent the area of the shaded region is,

$6x^2+8x$

Learn more about the area of rectangle here;

https://brainly.com/question/11202023