What is the area of the shaded region given the area of the two squares?

Question

Given is a big square whose area is 4x^2. (2x cm each side)

Inside the big square, there is a small square whose are is 16. (4 cm each side)

Now, the region outside the smaller square, but inside the bigger square, is shaded. What is the area of the shaded region? Give the answer in a factored form... Thanks!

My answer was (2x-4)(2x+4). Am I right?

Answer 1

Yes, that's correct.  The area of the shaded region would be the area of the larger square minus the area of the smaller square, or 4x^2-16, which is the difference of two squares and factors to (2x-4)(2x+4).