Expand and Simplify (a + b)(a - b)

Here's the template filled in for the expression (a + b)(a - b):

Here is how to expand and simplify the expression (a + b)(a - b) using the FOIL method (also known as the distributive property). FOIL stands for First, Outside, Inside, and Last.

Step 1: Multiply the terms in the first parentheses with the terms in the second parentheses.

Multiply a by a: a * a = a^2
Multiply a by -b: a * -b = -ab
Multiply b by a: b * a = ba (which can be simplified to ab, since multiplication is commutative)
Multiply b by -b: b * -b = -b^2

Step 2: Combine the like terms (terms with the same variable exponent).

Combine the terms -ab and ab: -ab + ab = 0 (they cancel out)
Combine the terms a^2 and -b^2: a^2 - b^2

So, now we have: a^2 - b^2

The expanded and simplified expression is a^2 - b^2.