Question

factor the following expression.
$26u^{2}w^{6} + 13u^{9}w^{5}x^{8}$

Explanation:

Step1: Identify the GCF of coefficients and variables

First, find the greatest common factor (GCF) of the coefficients 26 and 13. The GCF of 26 and 13 is 13.
For the variables:

• For \( u \): the lowest power is \( u^2 \) (from \( 26u^2w^6 \)) and \( u^9 \) (from \( 13u^9w^5x^8 \)), so GCF for \( u \) is \( u^2 \).
• For \( w \): the lowest power is \( w^5 \) (from \( 13u^9w^5x^8 \)) and \( w^6 \) (from \( 26u^2w^6 \)), so GCF for \( w \) is \( w^5 \).
• For \( x \): only the second term has \( x \), so GCF for \( x \) is 1 (since the first term has no \( x \)).

So the GCF of the two terms is \( 13u^2w^5 \).

Step2: Factor out the GCF

Factor out \( 13u^2w^5 \) from each term:
\( 26u^2w^6 + 13u^9w^5x^8 = 13u^2w^5 \cdot 2w + 13u^2w^5 \cdot u^7x^8 \)

Step3: Apply distributive property

Using the distributive property \( ab + ac = a(b + c) \), we get:
\( 13u^2w^5(2w + u^7x^8) \)

Answer:

\( 13u^2w^5(2w + u^7x^8) \)