Question

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 1

Answer:

a) $x^2-9^2=(x+9)(x-9)$

b) $(3x+y)^2-(2y)^2=(3x+3y)(3x-y)$

c) $2^2-(x-1)^2=(1+x)(3-x)$

d) $(x+2)^2-(y-2)^2=(x+y)(x-y+4)$

Explanation:

Factor the expression using difference of two squares.

Formula:

$a^2-b^2=(a+b)(a-b)$

Part a)  x²-81

write 81 as perfect square.

$x^2-9^2$

$a\rightarrow x$

$b\rightarrow 9$

$x^2-9^2=(x+9)(x-9)$

Part b) (3x+y)² -(2y)²

$a\rightarrow 3x+y$

$b\rightarrow 2y$

$(3x+y)^2-(2y)^2=(3x+y+2y)(3x+y-2y)$

$(3x+y)^2-(2y)^2=(3x+3y)(3x-y)$

Part c) 4-(x-1)²

write 4 as perfect square,

$2^2-(x-1)^2$

$a\rightarrow 2$

$b\rightarrow x-1$

$2^2-(x-1)^2=(2+x-1)(2-x+1)$

$2^2-(x-1)^2=(1+x)(3-x)$

Part d) (x+2)²-(y-2)²

$a\rightarrow x+2$

$b\rightarrow y-2$

$(x+2)^2-(y-2)^2=(x+2+y-2)(x+2-y+2)$

$(x+2)^2-(y-2)^2=(x+y)(x-y+4)$