Expand the following:
(5 x+2 y) (2 x y+y+9 x+2 z)
(9 x+y+2 x y+2 z) (5 x+2 y) = 5 x (9 x+y+2 x y+2 z)+2 y (9 x+y+2 x y+2 z):
5 x (9 x+y+2 x y+2 z)+2 y (9 x+y+2 x y+2 z)
5 x (9 x+y+2 x y+2 z) = 5 x×9 x+5 x y+5 x×2 x y+5 x×2 z:
5×9 x x+5 x y+5×2 x x y+5×2 x z+2 y (9 x+y+2 x y+2 z)
5 x×9 x = 5 x^2×9:
5×9 x^2+5 x y+5×2 x x y+5×2 x z+2 y (9 x+y+2 x y+2 z)
5×9 = 45:
45 x^2+5 x y+5×2 x x y+5×2 x z+2 y (9 x+y+2 x y+2 z)
5 x×2 x y = 5 x^2×2 y:
45 x^2+5 x y+5×2 x^2 y+5×2 x z+2 y (9 x+y+2 x y+2 z)
5×2 = 10:
45 x^2+5 x y+10 x^2 y+5×2 x z+2 y (9 x+y+2 x y+2 z)
5×2 = 10:
45 x^2+5 x y+10 x^2 y+10 x z+2 y (9 x+y+2 x y+2 z)
2 y (9 x+y+2 x y+2 z) = 2 y×9 x+2 y y+2 y×2 x y+2 y×2 z:
45 x^2+5 x y+10 x^2 y+10 x z+2×9 y x+2 y y+2×2 y x y+2×2 y z
2×9 = 18:
45 x^2+5 x y+10 x^2 y+10 x z+18 y x+2 y y+2×2 y x y+2×2 y z
2 y y = 2 y^2:
45 x^2+5 x y+10 x^2 y+10 x z+18 y x+2 y^2+2×2 y x y+2×2 y z
2 y×2 x y = 2×2 y^2 x:
45 x^2+5 x y+10 x^2 y+10 x z+18 y x+2 y^2+2×2 y^2 x+2×2 y z
2×2 = 4:
45 x^2+5 x y+10 x^2 y+10 x z+18 y x+2 y^2+4 y^2 x+2×2 y z
2×2 = 4:
45 x^2+5 x y+10 x^2 y+10 x z+18 y x+2 y^2+4 y^2 x+4 y z
Grouping like terms, 45 x^2+5 x y+10 x^2 y+10 x z+18 y x+2 y^2+4 y^2 x+4 y z = 4 y z+10 x z+4 x y^2+2 y^2+10 x^2 y+(5 x y+18 x y)+45 x^2:
4 y z+10 x z+4 x y^2+2 y^2+10 x^2 y+(5 x y+18 x y)+45 x^2
5 (x y)+18 (x y) = 23 (x y):
Answer: |4yz + 10xz + 4y^2 + 2y^2 + 10x^2y + 23xy + 45x^2
