Questions: Factor the following expression. 24 u^3 w^9+18 u w^3 y^6

Transcript text: Factor the following expression. \[ 24 u^{3} w^{9}+18 u w^{3} y^{6} \]

Solution

Solution Steps

To factor out a monomial from the given polynomial, we need to find the greatest common divisor (GCD) of the coefficients and the lowest power of each variable that appears in all terms. Then, we factor out this GCD and the lowest powers of the variables from each term.

Step 1: Identify the Greatest Common Divisor (GCD)

To factor the polynomial \(24u^3w^9 + 18uw^3y^6\), we first identify the GCD of the coefficients and the lowest power of each variable that appears in all terms.

The GCD of the coefficients \(24\) and \(18\) is \(6\).
The lowest power of \(u\) is \(u\).
The lowest power of \(w\) is \(w^3\).
The variable \(y\) only appears in the second term, so it does not affect the GCD.

Step 2: Factor Out the GCD

We factor out \(6uw^3\) from each term in the polynomial:

\[ 24u^3w^9 + 18uw^3y^6 = 6uw^3(4u^2w^6 + 3y^6) \]