Question

From 6x2−7xy+8y2 subtract the sum of x2−3xy−y2 and 2x2+5xy−4y2

Every 2 is meant to be the power of 2

Answer 1

13 y^2 - 9 x y + 3 x^2

Explanation:

Simplify the following:

6 x^2 - 7 x y + 8 y^2 - (x^2 - 3 x y - y^2) - (2 x^2 + 5 x y - 4 y^2)

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

6 x^2 - 7 x y + 8 y^2 + -x^2 + 3 x y + y^2 - (2 x^2 + 5 x y - 4 y^2)

-(2 x^2 + 5 x y - 4 y^2) = -2 x^2 - 5 x y + 4 y^2:

6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 + -2 x^2 - 5 x y + 4 y^2

Grouping like terms, 6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 - 2 x^2 - 5 x y + 4 y^2 = (8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2):

(8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)

8 y^2 + y^2 + 4 y^2 = 13 y^2:

13 y^2 + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)

x y (-7) + x y 3 + x y (-5) = -9 x y:

13 y^2 + -9 x y + (6 x^2 - x^2 - 2 x^2)

6 x^2 - x^2 - 2 x^2 = 3 x^2:

Answer: 13 y^2 - 9 x y + 3 x^2