Statement Simplify the following expressions: (a) (2x+3)2−(2x−3)2(2x+3)^2-(2x-3)^2(2x+3)2−(2x−3)2 (b) (x2−1)(x2+1)(x^2-1)(x^2+1)(x2−1)(x2+1) Solution (a) Difference of squares: (2x+3)2−(2x−3)2=[(2x+3)+(2x−3)] [(2x+3)−(2x−3)]=(4x)(6)=24x(2x+3)^2-(2x-3)^2=[(2x+3)+(2x-3)]\,[(2x+3)-(2x-3)]=(4x)(6)=24x(2x+3)2−(2x−3)2=[(2x+3)+(2x−3)][(2x+3)−(2x−3)]=(4x)(6)=24x. (b) (x2−1)(x2+1)=x4−1(x^2-1)(x^2+1)=x^4-1(x2−1)(x2+1)=x4−1. (a) 24x;(b) x4−1\boxed{(a)\ 24x;\qquad (b)\ x^4-1}(a) 24x;(b) x4−1