Question: Factor the following expression. \[ 26w^2 x^2 y^6 + 16w^9 x^5 \]

Factor the following expression.

\[ 26w^2 x^2 y^6 + 16w^9 x^5 \]

Solution

To factor the expression \( 26w^2x^2y^6 + 16w^9x^5 \), follow these steps: Identify the greatest common factor (GCF) of the terms. The GCF of the coefficients 26 and 16 is 2. The GCF of the \( w \) terms is \( w^2 \). The GCF of the \( x \) terms is \( x^2 \). There is no \( y \) in the second term, so it doesn’t contribute to the GCF. Thus, the GCF of the entire expression is \( 2w^2x^2 \). Factor out the GCF from the expression: \[ 26w^2x^2y^6 + 16w^9x^5 = 2w^2x^2(13y^6 + 8w^7x^3) \] This is the factored form of the expression.