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) x²-81
write 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]
