IDNLearn.com: Where curiosity meets clarity and questions find their answers. Discover trustworthy solutions to your questions quickly and accurately with help from our dedicated community of experts.
Sagot :
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.
### 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.
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.