Chapter 1 - Section 1.3 - Algebraic Expressions - 1.3 Exercises - Page 34: 114

$(a+1)(a-1)(b+2)(b-2)$

$Factor$ $the$ $expression$ $completely:$ $(a^2-1)b^2 - 4(a^2-1)$ Factor out $(a^2-1)$ from both terms $(a^2-1)(b^2-4)$ Use the Difference of Squares Formula for both binomials Difference of Squares Formula: $(A^2-B^2) = (A-B)(A+B)$ $(a^2-1) = (a+1)(a-1)$ $(b^2-4) = (b+2)(b-2)$ $= (a+1)(a-1)(b+2)(b-2)$