Question

① $8xy^{2}+9x^{2}y - xy$ ① $15x^{6}+ax^{3}y$

Explanation:

First Expression: \( 8xy^2 + 9x^2y - xy \)

Step1: Identify the GCF

The greatest common factor (GCF) of \( 8xy^2 \), \( 9x^2y \), and \( -xy \) is \( xy \).

Step2: Factor out the GCF

Factor \( xy \) from each term:
\( xy(8y + 9x - 1) \)

Second Expression: \( 15x^6 + 9x^3y \)

Step1: Identify the GCF

The GCF of \( 15x^6 \) and \( 9x^3y \) is \( 3x^3 \).

Step2: Factor out the GCF

Factor \( 3x^3 \) from each term:
\( 3x^3(5x^3 + 3y) \)

Answer:

• For \( 8xy^2 + 9x^2y - xy \): \( \boldsymbol{xy(8y + 9x - 1)} \)
• For \( 15x^6 + 9x^3y \): \( \boldsymbol{3x^3(5x^3 + 3y)} \)