Chapter 1 - Section 1.3 - Algebraic Expressions - 1.3 Exercises - Page 34: 111

$4ab$

$Factor$ $the$ $expression$ $completely:$ $(a+b)^2-(a-b)^2$ Square of a Sum Formula: $(A+B)^2 = A^2 + 2AB + B^2$ Square of a Difference Formula: $(A-B)^2 = A^2 - 2AB + B^2$ Simplify both terms by using the Square of a Sum and Square of a difference Product Formulas $(a^2+2ab+b^2)$ - $(a^2 - 2ab + b^2)$ Distribute the minus sign (-1) to $(a^2 - 2ab + b^2)$ $(a^2 + 2ab + b^2)$ + $(-a^2 + 2ab - b^2)$ Remove the parenthesis and simplify $a^2 + 2ab + b^2 - a^2 + 2ab - b^2$ = $4ab$