Simplify the following:
(2 x^2 (10 x^2 - 3 x y + 4 y^2))/(3) - (3 x^2 + 5 x y)
Factor x out of 3 x^2 + 5 x y:
(2 x^2 (10 x^2 - 3 x y + 4 y^2))/3 - x (3 x + 5 y)
Put each term in (2 x^2 (10 x^2 - 3 x y + 4 y^2))/3 - x (3 x + 5 y) over the common denominator 3: (2 x^2 (10 x^2 - 3 x y + 4 y^2))/3 - x (3 x + 5 y) = (2 x^2 (10 x^2 - 3 x y + 4 y^2))/3 - (3 x (3 x + 5 y))/3:
(2 x^2 (10 x^2 - 3 x y + 4 y^2))/3 - (3 x (3 x + 5 y))/3
(2 x^2 (10 x^2 - 3 x y + 4 y^2))/3 - (3 x (3 x + 5 y))/3 = (2 x^2 (10 x^2 - 3 x y + 4 y^2) - 3 x (3 x + 5 y))/3:
(2 x^2 (10 x^2 - 3 x y + 4 y^2) - 3 x (3 x + 5 y))/3
Factor x out of 2 x^2 (10 x^2 - 3 x y + 4 y^2) - 3 x (3 x + 5 y), resulting in x (2 (10 x^2 - 3 x y + 4 y^2) x^(2 - 1) - 3 (3 x + 5 y)):
x (2 x^(2 - 1) (10 x^2 - 3 x y + 4 y^2) - 3 (3 x + 5 y))/3
2 - 1 = 1:
(x (2 x (10 x^2 - 3 x y + 4 y^2) - 3 (3 x + 5 y)))/3
2 x (10 x^2 - 3 x y + 4 y^2) = 20 x^3 - 6 x^2 y + 8 x y^2:
(x (20 x^3 - 6 x^2 y + 8 x y^2 - 3 (3 x + 5 y)))/3
-3 (3 x + 5 y) = -9 x - 15 y:
Answer: |(x (20 x^3 - 6 x^2 y + 8 x y^2 + -9 x - 15 y))/3
