Question

factor the following expression.
$20u^5x^2y^3 - 5u^8x^7$

Explanation:

Step1: Identify GCF of coefficients and variables

Coefficients: GCF of 20 and 5 is 5.
Variables: For \( u \): minimum exponent is 5 (\( u^5 \) in first term, \( u^8 \) in second).
For \( x \): minimum exponent is 2 (\( x^2 \) in first term, \( x^7 \) in second).
For \( y \): only in first term, so \( y^0 = 1 \) (not included in GCF for variables common to both terms).
GCF: \( 5u^5x^2 \).

Step2: Divide each term by GCF

First term: \( \frac{20u^5x^2y^3}{5u^5x^2} = 4y^3 \).
Second term: \( \frac{-5u^8x^7}{5u^5x^2} = -u^3x^5 \).

Step3: Write factored form

Factor out GCF: \( 5u^5x^2(4y^3 - u^3x^5) \).

Answer:

\( 5u^5x^2(4y^3 - u^3x^5) \)