(a+b)(x-y)-(a-b)(x+y) (a+b)(x-y) = (ax + bx - ay - by) (a-b)(x+y) = (ax - bx + ay - by) (ax + bx - ay - by) - (ax - bx + ay - by) ax + bx - y - by - ax + bx - ay + by ax cancels by cancels bx - y + bx - ay 2bx - ay - y 2bx - y(a - 1)
Use the distributive property on the first two terms and then separately on the last two terms. Don't let the subtraction in the middle throw you off! Evaluate normally and then "distribute the negative sign" to each term: ax - ay + bx - by - (ax + ay -bx -by) = ax - ay + bx - by - ax - ay + bx + by = 2bx - 2ay
