Question

Which expressions are completely factored?

Select each correct answer.



Responses

20y7+10y2=5y(4y6+2y)
20 y begin power 7 end power plus 10 y squared equals 5 y left parenthesis 4 y begin power 6 end power plus 2 y right parenthesis

32y10−24=8(4y10−3)
32 y begin power 10 end power minus 24 equals 8 left parenthesis 4 y begin power 10 end power minus 3 right parenthesis

18y3−6y=3y(6y2−2)
18 y cubed minus 6 y equals 3 y left parenthesis 6 y squared minus 2 right parenthesis

16y5+12y3=4y3(4y2+3)

Answer 1

To determine which expressions are completely factored, we need to check if there are any further factors that could be factored out from the given expressions. Here are the responses analyzed one by one:

1. **20y^7 + 10y^2 = 5y(4y^6 + 2y)**
- This expression is factored out correctly, but the term inside the parentheses, \(4y^6 + 2y\), can be factored further: \(2y(2y^5 + 1)\). So this expression is **not completely factored**.

2. **32y^{10} - 24 = 8(4y^{10} - 3)**
- This expression is factored correctly. The term inside parentheses, \(4y^{10} - 3\), cannot be factored further into rational factors. Thus, this expression is **completely factored**.

3. **18y^3 - 6y = 3y(6y^2 - 2)**
- This expression is factored correctly, but the term inside the parentheses, \(6y^2 - 2\), can be factored further as \(2(3y^2 - 1)\). Thus, this expression is **not completely factored**.

4. **16y^5 + 12y^3 = 4y^3(4y^2 + 3)**
- This expression is factored correctly, and the term inside the parentheses, \(4y^2 + 3\), cannot be factored further. Hence, this expression is **completely factored**.

### Final Answers
- **Completely factored expressions**:
- 32y^{10} - 24 = 8(4y^{10} - 3)
- 16y^5 + 12y^3 = 4y^3(4y^2 + 3)