What does the expression (a+b)(a+b) equal?

The expression ((a+b)(a+b)) represents the square of the binomial (a + b). To understand why the correct answer is (a^2 + 2ab + b^2), consider the process of multiplying the binomial by itself, which is often referred to as "FOIL" (First, Outside, Inside, Last).

1. First: Multiply the first terms in each binomial, which gives you (a \cdot a = a^2).
2. Outside: Multiply the outer terms, leading to (a \cdot b = ab).

3. Inside: Multiply the inner terms, resulting in (b \cdot a = ab).
4. Last: Finally, multiply the last terms in each binomial, yielding (b \cdot b = b^2).

Now, combine all these products:

• From the First we have (a^2).
• From the Outside and Inside we combine (ab + ab) to give (2ab).
• From the Last we have (b^2).

Putting this all together results in the expression (a^2 + 2ab +