Question

Write the expression -3x 2 + 2y 2 + 5xy - 2y + 5x 2 - 3y 2 in simplest form. Then, answer the following questions using complete sentences. A)How many terms are in the simplified expression? B) How many of the terms in the simplified expression are negative?

Answer 1

Simplify the following:

-3 x^2 + 2 y^2 + 5 x y - 2 y + 5 x^2 - 3 y^2

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

(2 y^2 - 3 y^2) + 5 x y - 2 y + (5 x^2 - 3 x^2)

2 y^2 - 3 y^2 = -y^2:

-y^2 + 5 x y - 2 y + (5 x^2 - 3 x^2)

5 x^2 - 3 x^2 = 2 x^2:

Answer: -y^2 + 5 x y - 2 y + 2 x^2