Question

marcus finds that $left(3x^{2}-2y^{2}+5x
ight)+left(4x^{2}+12y^{2}-7x
ight)=7x^{2}-10y^{2}-2x$. 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

$3x^2 + 4x^2 = 7x^2$

Step2: Combine $y^2$ terms

$-2y^2 + 12y^2 = 10y^2$

Step3: Combine $x$ terms

$5x + (-7x) = -2x$

Step4: Compare to Marcus's result

Marcus got $-10y^2$ instead of $10y^2$.

Answer:

He combined the terms $-2y^2$ and $12y^2$ incorrectly.