Sure, let's factor the expression [tex]\( 30u^5x^8 + 24ux^5y^2 \)[/tex] step-by-step.
1. Identify the common terms:
First, we observe the given expression to find any common factors in both terms.
[tex]\[
30u^5x^8 + 24ux^5y^2
\][/tex]
2. Extract the numerical greatest common divisor (GCD):
The coefficients are 30 and 24. The greatest common divisor of 30 and 24 is 6.
3. Identify the common variables and their lowest powers:
- For [tex]\( u^5 \)[/tex] and [tex]\( u \)[/tex], the common variable is [tex]\( u \)[/tex] with the lowest power being [tex]\( u \)[/tex].
- For [tex]\( x^8 \)[/tex] and [tex]\( x^5 \)[/tex], the common variable is [tex]\( x \)[/tex] with the lowest power being [tex]\( x^5 \)[/tex].
So the common factor between the terms is [tex]\( 6ux^5 \)[/tex].
4. Factor out the common factor:
We factor [tex]\( 6ux^5 \)[/tex] out from each term:
[tex]\[
30u^5x^8 = 6ux^5 \cdot 5u^4x^3
\][/tex]
[tex]\[
24ux^5y^2 = 6ux^5 \cdot 4y^2
\][/tex]
5. Write the factored expression:
After factoring [tex]\( 6ux^5 \)[/tex] out of both terms, we have:
[tex]\[
30u^5x^8 + 24ux^5y^2 = 6ux^5 (5u^4x^3) + 6ux^5 (4y^2)
\][/tex]
Combine the terms inside the parentheses:
[tex]\[
= 6ux^5 (5u^4x^3 + 4y^2)
\][/tex]
So, the factored form of the expression [tex]\( 30u^5x^8 + 24ux^5y^2 \)[/tex] is:
[tex]\[
6ux^5 (5u^4x^3 + 4y^2)
\][/tex]
