Question

Place the indicated product in the proper location on the grid. (a^x - b^y)(a^x + b^y)

Answer 1

`(a^x - b^y)(a^x + b^y)=a^(2x)-b^(2y)`

Explanation:

Polynomial Notable Products

Some products of polynomials are so frequent that the literature has compiled them into a special set of formulas for the mathematicians to easily use them. One of the best-known formulas is the so-called product of the sum by the difference of binomials, i.e.

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

We are given the following expression

`(a^x - b^y)(a^x + b^y)`

Applying the formula:

`(a^x - b^y)(a^x + b^y)=(a^x)^2-(b^y)^2=a^(2x)-b^(2y)`

Thus

`\boxed{(a^x - b^y)(a^x + b^y)=a^(2x)-b^(2y)}`