4(x-y)^2-12(x-y)(x+y)+9(x+y)^2 ​

Answer:(x + 5 y)^2Step-by-step explanation:Simplify the following:4 (x - y)^2 - 12 (x - y) (x + y) + 9 (x + y)^2(x - y) (x - y) = (x) (x) + (x) (-y) + (-y) (x) + (-y) (-y) = x^2 - x y - x y + y^2 = x^2 - 2 x y + y^2:4 x^2 - 2 x y + y^2 - 12 (x - y) (x + y) + 9 (x + y)^24 (x^2 - 2 x y + y^2) = 4 x^2 - 8 x y + 4 y^2:4 x^2 - 8 x y + 4 y^2 - 12 (x - y) (x + y) + 9 (x + y)^2(x + y) (x - y) = (x) (x) + (x) (-y) + (y) (x) + (y) (-y) = x^2 - x y + x y - y^2 = x^2 - y^2:4 x^2 - 8 x y + 4 y^2 - 12 x^2 - y^2 + 9 (x + y)^2-12 (x^2 - y^2) = 12 y^2 - 12 x^2:4 x^2 - 8 x y + 4 y^2 + 12 y^2 - 12 x^2 + 9 (x + y)^2(x + y) (x + y) = (x) (x) + (x) (y) + (y) (x) + (y) (y) = x^2 + x y + x y + y^2 = x^2 + 2 x y + y^2:4 x^2 - 8 x y + 4 y^2 - 12 x^2 + 12 y^2 + 9 x^2 + 2 x y + y^2Grouping like terms, 4 x^2 - 8 x y + 4 y^2 - 12 x^2 + 12 y^2 + 9 (x^2 + 2 x y + y^2) = 9 (x^2 + 2 x y + y^2) + (4 y^2 + 12 y^2) - 8 x y + (4 x^2 - 12 x^2):9 (x^2 + 2 x y + y^2) + (4 y^2 + 12 y^2) - 8 x y + (4 x^2 - 12 x^2)4 y^2 + 12 y^2 = 16 y^2:9 (x^2 + 2 x y + y^2) + 16 y^2 - 8 x y + (4 x^2 - 12 x^2)4 x^2 - 12 x^2 = -8 x^2:9 (x^2 + 2 x y + y^2) + 16 y^2 - 8 x y + -8 x^29 (x^2 + 2 x y + y^2) = 9 x^2 + 18 x y + 9 y^2:9 x^2 + 18 x y + 9 y^2 + 16 y^2 - 8 x y - 8 x^2Grouping like terms, 9 x^2 + 18 x y + 9 y^2 + 16 y^2 - 8 x y - 8 x^2 = (9 y^2 + 16 y^2) + (18 x y - 8 x y) + (9 x^2 - 8 x^2):(9 y^2 + 16 y^2) + (18 x y - 8 x y) + (9 x^2 - 8 x^2)9 y^2 + 16 y^2 = 25 y^2:25 y^2 + (18 x y - 8 x y) + (9 x^2 - 8 x^2)x y 18 + x y (-8) = 10 x y:25 y^2 + 10 x y + (9 x^2 - 8 x^2)9 x^2 - 8 x^2 = x^2:25 y^2 + 10 x y + x^2The factors of 25 that sum to 10 are 5 and 5. So, 25 y^2 + 10 x y + x^2 = (x + 5 y) (x + 5 y):(x + 5 y) (x + 5 y)(x + 5 y) (x + 5 y) = (x + 5 y)^2:Answer:  (x + 5 y)^2