Question

add the polynomials.
$(3x^{2y} - 3x^y + 6) + (-9x^{2y} + 6x^y - 9)$
$(3x^{2y} - 3x^y + 6) + (-9x^{2y} + 6x^y - 9) = square$
(simplify your answer. do not factor.)

Explanation:

Step1: Identify like terms

The polynomials are \((3x^{2y} - 3x^y + 6)\) and \((-9x^{2y} + 6x^y - 9)\). The like terms are \(3x^{2y}\) and \(-9x^{2y}\), \(-3x^y\) and \(6x^y\), \(6\) and \(-9\).

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

\(3x^{2y}+(-9x^{2y}) = 3x^{2y}-9x^{2y}=-6x^{2y}\)

Step3: Combine like terms for \(x^y\)

\(-3x^y + 6x^y=3x^y\)

Step4: Combine constant terms

\(6+(-9)=6 - 9=-3\)

Step5: Combine all results

Putting it together, we get \(-6x^{2y}+3x^y - 3\)

Answer:

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