Question

1. add or subtract the polynomials.

(7x²y² - 6x³ + xy) - (5x²y² - x³ + xy + x)
enter your answer.

Explanation:

Step1: Distribute the negative sign

We need to distribute the negative sign to each term inside the second parentheses. So we have:
\(7x^{2}y^{2}-6x^{3}+xy - 5x^{2}y^{2}+x^{3}-xy - x\)

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

The terms with \(x^{2}y^{2}\) are \(7x^{2}y^{2}\) and \(-5x^{2}y^{2}\). Combining them:
\(7x^{2}y^{2}-5x^{2}y^{2}=(7 - 5)x^{2}y^{2}=2x^{2}y^{2}\)

Step3: Combine like terms for \(x^{3}\) terms

The terms with \(x^{3}\) are \(-6x^{3}\) and \(x^{3}\). Combining them:
\(-6x^{3}+x^{3}=(-6 + 1)x^{3}=-5x^{3}\)

Step4: Combine like terms for \(xy\) terms

The terms with \(xy\) are \(xy\) and \(-xy\). Combining them:
\(xy-xy = 0\)

Step5: Write the remaining term

The remaining term is \(-x\). Now, combine all the results:
\(2x^{2}y^{2}-5x^{3}-x\) (we can also rearrange the terms in standard form as \(-5x^{3}+2x^{2}y^{2}-x\))

Answer:

\(-5x^{3}+2x^{2}y^{2}-x\) (or \(2x^{2}y^{2}-5x^{3}-x\))