Question

factor the following expression.
$14uw^{5}x^{9} + 18u^{8}w^{8}$

Explanation:

Step1: Find the GCF of coefficients and variables

First, find the greatest common factor (GCF) of the coefficients 14 and 18. The factors of 14 are 1, 2, 7, 14 and the factors of 18 are 1, 2, 3, 6, 9, 18. So the GCF of 14 and 18 is 2.

For the variable \( u \), the lowest power between \( u^1 \) and \( u^8 \) is \( u^1 \).

For the variable \( w \), the lowest power between \( w^5 \) and \( w^8 \) is \( w^5 \).

There is no \( x \) in the second term, so \( x \) is not part of the GCF.

So the GCF of the two terms is \( 2uw^5 \).

Step2: Factor out the GCF

Factor out \( 2uw^5 \) from each term:

\( 14uw^5x^9 + 18u^8w^8 = 2uw^5(7x^9 + 9u^7w^3) \)

Answer:

\( 2uw^5(7x^9 + 9u^7w^3) \)