Question

expressions-polynomials-evaluate add subtract po
(1 point)
perform the operation
$(-5x^2y + 3y + 1) + (-x^2y - 6x - 3)$
and combine like terms. simplify your answer as much as possible.
answer: $-6x^2y - 6x + 3y - 2$

Explanation:

Step1: Remove parentheses

To add the two polynomials, we first remove the parentheses. Since there is a plus sign in front of the second parentheses, the signs of the terms inside remain the same. So we have:
\(-5x^{2}y + 3y + 1 - x^{2}y - 6x - 3\)

Step2: Combine like terms for \(x^{2}y\) terms

The terms with \(x^{2}y\) are \(-5x^{2}y\) and \(-x^{2}y\). Combining them, we add their coefficients: \(-5 - 1 = -6\), so we get \(-6x^{2}y\).

Step3: The term with \(x\)

There is only one term with \(x\), which is \(-6x\), so it remains as is.

Step4: The term with \(y\)

There is only one term with \(y\) (excluding the \(x^{2}y\) terms), which is \(3y\), so it remains as is.

Step5: Combine constant terms

The constant terms are \(1\) and \(-3\). Combining them, we have \(1 - 3 = -2\).

Step6: Combine all terms

Putting all the combined terms together, we get:
\(-6x^{2}y - 6x + 3y - 2\)

Answer:

\(-6x^{2}y - 6x + 3y - 2\)