Question

topic: operations with polynomials
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
simplify \\((3x^2 + 2y^2 - 5x + y) + (2x^2 - 2xy - 2y^2 - 5x + 3y)\\)
\\(\bigcirc\\) \\(5x^2 - 2xy - 10x + 4y\\)
\\(\bigcirc\\) \\(5x^2 - 2xy + y^2 + 4y\\)
\\(\bigcirc\\) \\(5x^2 + y^2 - 10x\\)
\\(\bigcirc\\) \\(5x^2 - 2xy + y^2 - 10x\\)

Explanation:

Step1: Combine \(x^2\) terms

\(3x^2 + 2x^2 = 5x^2\)

Step2: Combine \(y^2\) terms

\(2y^2 - 2y^2 = 0\)

Step3: Combine \(x\) terms

\(-5x - 5x = -10x\)

Step4: Combine \(y\) terms

\(y + 3y = 4y\)

Step5: Keep the \(xy\) term

\(-2xy\) (no other \(xy\) terms to combine)

Step6: Combine all terms

\(5x^2 - 2xy - 10x + 4y\)

Answer:

\(5x^2 - 2xy - 10x + 4y\) (corresponding to the first option: \(5x^2 - 2xy - 10x + 4y\))