Certainly! Let's walk through the factoring of each expression step-by-step.
### 1. Factor [tex]\( 10(x + y + z_3) \)[/tex]
The given expression is [tex]\( 10x + 10y + 10z_3 \)[/tex]. Notice that each term has a common factor of [tex]\( 10 \)[/tex].
- Step 1: Identify the common factor
[tex]\[
10x + 10y + 10z_3 \implies 10(x + y + z_3)
\][/tex]
So, the factored form is:
[tex]\[
10(x + y + z_3)
\][/tex]
### 2. Factor [tex]\( 25x^2 y^3 - 25xy^3 \)[/tex]
The given expression is [tex]\( 25x^2 y^3 - 25xy^3 \)[/tex]. Notice that each term has a common factor of [tex]\( 25xy^3 \)[/tex].
- Step 1: Identify the common factor
[tex]\[
25x^2 y^3 - 25xy^3 \implies 25xy^3(x - 1)
\][/tex]
So, the factored form is:
[tex]\[
25xy^3(x - 1)
\][/tex]
### 3. Factor [tex]\( 3x^2 y^{-4} z^5 + 15x^2 z^3 \)[/tex]
The given expression is [tex]\( 3x^2 y^{-4} z^5 + 15x^2 z^3 \)[/tex]. Notice that each term has a common factor of [tex]\( 3x^2 z^3 \)[/tex].
- Step 1: Identify the common factor
[tex]\[
3x^2 y^{-4} z^5 + 15x^2 z^3 \implies 3x^2 z^3(y^{-4} z^2 + 5)
\][/tex]
[tex]\[
\implies 3x^2 z^3(\frac{z^2}{y^4} + 5)
\][/tex]
Simplify further:
[tex]\[
3x^2 z^3 \left( \frac{5y^4 + z^2}{y^4} \right)
\][/tex]
So, the factored form is:
[tex]\[
3x^2 z^3 \frac{5y^4 + z^2}{y^4}
\][/tex]
### Summary of factored forms:
1. [tex]\( 10(x + y + z_3) \)[/tex]
2. [tex]\( 25xy^3 (x - 1) \)[/tex]
3. [tex]\( 3x^2 z^3 \frac{5y^4 + z^2}{y^4} \)[/tex]
These are the expressions factored step-by-step.
