if the sides of the sqaure are represented by a and b what is the area of the remaining glass when the smaller square is cut from the larger square? write answer in factored form

i don't understand because of the variables

It looks like the side of the larger square is a.

The side of the larger square is b.
Area of larger square = a^2
Area of smaller square = b^2

Area of remaining glass is a^2 - b^2

Factor thatbexpression

how do you factor it?

That's the difference of two squares.

(a+ b)(a - b)

Remember?

To understand this problem, let's start by visualizing the situation. You have a larger square with side lengths represented by 'a' units. And within this larger square, there is a smaller square with side lengths represented by 'b' units.

To find the area of the remaining glass when the smaller square is cut from the larger square, we need to calculate the difference in their areas.

The area of a square is determined by multiplying its two sides together. So, the area of the larger square is:

Area of the larger square = a * a = a^2 square units

Similarly, the area of the smaller square is:

Area of the smaller square = b * b = b^2 square units

To find the area of the remaining glass, we subtract the area of the smaller square from the area of the larger square:

Area of the remaining glass = Area of the larger square - Area of the smaller square
= a^2 - b^2 square units

Now, the question asks us to write the answer in factored form. To do this, we can factorize the expression for the area of the remaining glass.

By applying the difference of squares formula, we get:

a^2 - b^2 = (a + b)(a - b)

So, the area of the remaining glass can be expressed in factored form as:

(a + b)(a - b) square units