Question

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

Use the difference of two squares identity to help you rewrite the expression in factored form. Be sure to simplify each factor.

Answer 1

The difference of two squares factoring pattern states that a difference of two squares can be factored as follows:

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

So, whenever you recognize the two terms of a subtraction to be two squares, you can factor it as the sum of the roots multiplied by the difference of the roots.

In this case, the squares are obvious:
`(x+2)^2` is the square of
`x+2`, and
`(y+2)^2` is the square of
`y+2`

So, we can factor the expression as

`(x+2)^2 - (y+2)^2 = [(x+2)+(y+2)] - [(x+2)+(y+2)]`

(the round parenthesis aren't necessary, I used them only to make clear the two terms)

We can simplify the expression summing like terms:

`(x+2)^2 - (y+2)^2 = [(x+2)+(y+2)][(x+2)-(y+2)] = (x+y+4)(x-y)`