Question

1. $6n^2 - 2n - 3 + 5n^2 - 9n - 6$
2. $-12x^2y - 3x^2y$
3. $19x^2y - 4xy^2 + 5xy^2 - 16x^2y$

Explanation:

Problem 14: \(6n^2 - 2n - 3 + 5n^2 - 9n - 6\)

Step1: Combine like terms for \(n^2\)

\(6n^2 + 5n^2 = (6 + 5)n^2 = 11n^2\)

Step2: Combine like terms for \(n\)

\(-2n - 9n = (-2 - 9)n = -11n\)

Step3: Combine constant terms

\(-3 - 6 = -9\)

Step4: Combine all results

\(11n^2 - 11n - 9\)

Step1: Combine like terms

\(-12x^2y - 3x^2y = (-12 - 3)x^2y = -15x^2y\)

Step1: Combine like terms for \(x^2y\)

\(19x^2y - 16x^2y = (19 - 16)x^2y = 3x^2y\)

Step2: Combine like terms for \(xy^2\)

\(-4xy^2 + 5xy^2 = (-4 + 5)xy^2 = xy^2\)

Step3: Combine all results

\(3x^2y + xy^2\)

Answer:

\(11n^2 - 11n - 9\)

Problem 16: \(-12x^2y - 3x^2y\)