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

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)`