Question

marcus finds that ((3x^2 - 2y^2 + 5x) + (4x^2 + 12y^2 - 7x) = 7x^2 - 10y^2 - 2x). what error did marcus make?

• he combined the terms (5x) and (-7x) incorrectly.
• he combined the terms (3x^2) and (4x^2) incorrectly.
• he combined the terms (-2y^2) and (12y^2) incorrectly.
• he subtracted the polynomials instead of adding.

Explanation:

Step1: Combine \(x^2\) terms

\(3x^2 + 4x^2 = 7x^2\) (correct as Marcus did)

Step2: Combine \(y^2\) terms

\(-2y^2 + 12y^2 = 10y^2\) (Marcus got \(-10y^2\), wrong)

Step3: Combine \(x\) terms

\(5x - 7x = -2x\) (correct as Marcus did)

Step4: Check operation

Marcus added \(x^2\) and \(x\) terms correctly, only \(y^2\) combination was wrong.

Answer:

C. He combined the terms \(-2y^2\) and \(12y^2\) incorrectly.