The problem asks to state the formulas for the following expressions: $(a + b)^2$ $(a - b)^2$ $a^2 - b^2$ $a^3 - b^3$

1. Problem Description

The problem asks to state the formulas for the following expressions:

$(a + b)^2$

$(a - b)^2$

$a^2 - b^2$

$a^3 - b^3$

2. Solution Steps

We need to expand each of the given expressions.

$(a + b)^2 = (a + b)(a + b) = a^2 + ab + ba + b^2 = a^2 + 2ab + b^2$

$(a - b)^2 = (a - b)(a - b) = a^2 - ab - ba + b^2 = a^2 - 2ab + b^2$

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

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

3. Final Answer

$(a + b)^2 = a^2 + 2ab + b^2$

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

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

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$