Simplify the given expression. (16x^2 + 15xy – 19y^2) – (3x^2 – 3xy)

-19 y^2 + 18 x y + 13 x^2

Step-by-step explanation:

Simplify the following:

16 x^2 + 15 x y - 19 y^2 - (3 x^2 - 3 x y)

Factor 3 x out of 3 x^2 - 3 x y:

16 x^2 + 15 x y - 19 y^2 - 3 x (x - y)

-3 x (x - y) = 3 x y - 3 x^2:

16 x^2 + 15 x y - 19 y^2 + 3 x y - 3 x^2

Grouping like terms, 16 x^2 + 15 x y - 19 y^2 - 3 x^2 + 3 x y = -19 y^2 + (15 x y + 3 x y) + (16 x^2 - 3 x^2):

-19 y^2 + (15 x y + 3 x y) + (16 x^2 - 3 x^2)

x y 15 + x y 3 = 18 x y:

-19 y^2 + 18 x y + (16 x^2 - 3 x^2)

16 x^2 - 3 x^2 = 13 x^2:

 -19 y^2 + 18 x y + 13 x^2