Use the difference of two squares identity to factor each of the following expressions. (a) x²-81 (b) (3x+y)² -(2y)² (c) 4-(x-1)² (d) (x+2)²-(y-2)²

Answer: a) [tex]x^2-9^2=(x+9)(x-9)[/tex]b) [tex](3x+y)^2-(2y)^2=(3x+3y)(3x-y)[/tex]c) [tex]2^2-(x-1)^2=(1+x)(3-x)[/tex]d) [tex](x+2)^2-(y-2)^2=(x+y)(x-y+4)[/tex]Explanation: Factor the expression using difference of two squares. Formula: [tex]a^2-b^2=(a+b)(a-b)[/tex] Part a)  x²-81write 81 as perfect square.[tex]x^2-9^2[/tex][tex]a\rightarrow x[/tex][tex]b\rightarrow 9[/tex][tex]x^2-9^2=(x+9)(x-9)[/tex]Part b) (3x+y)² -(2y)²[tex]a\rightarrow 3x+y[/tex][tex]b\rightarrow 2y[/tex][tex](3x+y)^2-(2y)^2=(3x+y+2y)(3x+y-2y)[/tex][tex](3x+y)^2-(2y)^2=(3x+3y)(3x-y)[/tex]Part c) 4-(x-1)² write 4 as perfect square, [tex]2^2-(x-1)^2[/tex][tex]a\rightarrow 2[/tex][tex]b\rightarrow x-1[/tex][tex]2^2-(x-1)^2=(2+x-1)(2-x+1)[/tex][tex]2^2-(x-1)^2=(1+x)(3-x)[/tex]Part d) (x+2)²-(y-2)²[tex]a\rightarrow x+2[/tex][tex]b\rightarrow y-2[/tex][tex](x+2)^2-(y-2)^2=(x+2+y-2)(x+2-y+2)[/tex][tex](x+2)^2-(y-2)^2=(x+y)(x-y+4)[/tex]