X^2 + 4x + 4 - 9y^2

Question

factorise 

Answer 1

It might help to first factor the leading three terms.

 

(x+2)² - 9y²

 

The above has the form of a difference of squares. Generally a^2-b^2 is equivalent to (a+b)(a-b), so the above is equivalent to:

 

((x+2)-3y)((x+2)+3y)

 

We can use the associative property of addition and subtraction.

(x+2-3y)(x+2+3y)