JAMB 1994 · UME · Q11

Factorize $a^2x - b^2y - b^2x + a^2y$ .

Worked solution (try it first)

Group the terms with $a^2$ and those with $b^2$ : $(a^2x + a^2y) - (b^2x + b^2y)$ .
Take out the common factors: $a^2(x + y) - b^2(x + y) = (x + y)(a^2 - b^2)$ .
Factorise the difference of two squares: $(x + y)(a - b)(a + b)$ , option D.