Question

marcus finds that \\((3x^2 - 2y^2 + 5x) + (4x^2 + 12y^2 - 7x) = 7x^2 - 10y^2 - 2x\\).

• 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:

⚡ Using what you learned: adding and subtracting polynomials

Step 1: Identify like terms

Group the like terms from the two polynomials:

$$ (3x^2 + 4x^2) + (-2y^2 + 12y^2) + (5x - 7x) $$

Step 2: Combine each set of terms

Calculate the correct sum for each group:

• For \( x^2 \) terms:

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

• For \( y^2 \) terms:

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

• For \( x \) terms:

$$ 5x - 7x = -2x $$

The correct simplified expression is:

$$ 7x^2 + 10y^2 - 2x $$

Step 3: Compare with Marcus's result

Marcus's result:

$$ 7x^2 - 10y^2 - 2x $$

Comparing the terms:

• \( 7x^2 \) matches.
• \( -2x \) matches.
• Marcus wrote \( -10y^2 \) instead of \( 10y^2 \).

Therefore, he combined the terms \( -2y^2 \) and \( 12y^2 \) incorrectly.

Answer:

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