Simplify (4x^2 - 8xy + 2y^2) - (9x^2 - 4xy - 7y^2)

a. - 5x^2 + 4xy + 9y^2

b. - 5x^2 - 4xy + 9y^2

c. - 5x^2 + 12xy + 4y^2

d. - 5x^2 - 4xy - 5y^2

Choice b is correct answer.

Step-by-step explanation:

Given expression is:

(4x²-8xy+2y²) - (9x²-4xy-7y²)

We have to simplify above expression.

Step 1. Open small brackets and multiply negative sign to the terms of second small bracket.

4x² - 8xy + 2y² - 9x² + 4xy + 7y²

Step 2. Gather like terms

4x²-9x²-8xy+4xy+2y²+7y²

Step 3. Add the coefficients of like terms

(4-9) x² + (-8+4) xy + (2+7) y²

(-5) x² + (-4) xy + (9) y²

-5x²-4xy+9y² which is the final answer.

b

Step-by-step explanation:

Distribute parenthesis and collect like terms, noting that the second parenthesis is distributed by - 1

(4x² - 8xy + 2y²) - (9x² - 4xy - 7y²)

= 4x² - 8xy + 2y² - 9x² + 4xy + 7y² ← collect like terms

= (4x² - 9x²) + ( - 8xy + 4xy) + (2y² + 7y²)

= - 5x² - 4xy + 9y² → b