Question

Write an expression to represent the area of the shaded region in simplest from

Answer 1

We know that the area of a square/rectangle is the multiplication of its length by its width. We also know that this specific area does not include the blank region, therefore we need to subtract it from the area of the shaded region!

We can come up with two expressions:

Shaded Area:

`(5x + 2)(3x - 1)\\= 15x^2-5x+6x-2\\=15x^2+x-2`

Blank area:

`(x)(x+7)\\x^2+7x`

Now all we have to do is subtract the blank area's expression from the shaded area's and simplify since the question asks for the simplest form.

`(15x^2+x-2)-(x^2+7x)\\15x^2-x^2+x-7x-2\\14x^2-6x-2`

Therefore, your final answer should be:

14x^2 - 6x - 2