Question

kendall says the sum of \\((6x^2 + 4xy + 2y^2)\\) and \\((4x^2 - 2xy - 3y^2)\\) is \\((10x^2 + 2xy - 5y^2)\\). what error did kendall make?

• he combined the like terms \\(6x^2\\) and \\(4x^2\\) incorrectly.
• he combined the like terms \\(4xy\\) and \\(-2xy\\) incorrectly.
• he combined the like terms \\(2y^2\\) and \\(-3y^2\\) incorrectly.
• he subtracted the polynomials instead of adding.

Explanation:

⚡ Using what you learned: adding and subtracting polynomials

Step 1: Set up the sum

$$ (6x^2 + 4xy + 2y^2) + (4x^2 - 2xy - 3y^2) $$

Step 2: Group and combine like terms

Group the \(x^2\) terms:

$$ 6x^2 + 4x^2 = 10x^2 $$

Group the \(xy\) terms:

$$ 4xy + (-2xy) = 2xy $$

Group the \(y^2\) terms:

$$ 2y^2 + (-3y^2) = -1y^2 = -y^2 $$

Step 3: Compare with Kendall's result

Correct sum:

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

Kendall's sum:

$$ 10x^2 + 2xy - 5y^2 $$

Kendall wrote \(-5y^2\) instead of \(-y^2\) because he calculated \(2y^2 - 3y^2\) incorrectly (likely treating it as \(-2 - 3 = -5\) or adding their absolute values incorrectly).

Answer:

He combined the like terms \(2y^2\) and \(-3y^2\) incorrectly.