JAMB 1990 · UME · Q16

Factorize $9(x + y)^2 - 4(x - y)^2$ .

Worked solution (try it first)

Both terms are squares: $9(x + y)^2 = [3(x + y)]^2$ and $4(x - y)^2 = [2(x - y)]^2$ .
Difference of two squares: the first bracket is $3x + 3y - 2x + 2y$ , which is $x + 5y$ .
The second bracket is $3x + 3y + 2x - 2y$ , which is $5x + y$ .
So the expression is $(x + 5y)(5x + y)$ , option C.