Question

Which statements are true?

Select each correct answer.



Responses

15m3−6m=3m(5m2−6m)
15 m cubed minus 6 m equals 3 m left parenthesis 5 m squared minus 6 m right parenthesis

6m2+18m=6m2(1+3m)
6 m squared plus 18 m equals 6 m squared left parenthesis 1 plus 3 m right parenthesis

32m4+12m3=4m3(8m+3)
32 m begin power 4 end power plus 12 m cubed equals 4 m cubed left parenthesis 8 m plus 3 right parenthesis

40m6−4=4(10m6−1)
40 m begn power 6 end power minus 4 equals 4 left parenthesis 10 begin power 6 end power minus 1 right parenthesis

Answer 1

Let's analyze each statement one by one to determine if they are true.

1. **Statement**: \(15m^3 - 6m = 3m(5m^2 - 6m)\)

**Evaluation**:
- Left Side: \(15m^3 - 6m\)
- Right Side: \(3m(5m^2 - 6m) = 3m \cdot 5m^2 - 3m \cdot 6m = 15m^3 - 18m\)

**Result**: Left Side is not equal to Right Side. **False**.

2. **Statement**: \(6m^2 + 18m = 6m^2(1 + 3m)\)

**Evaluation**:
- Left Side: \(6m^2 + 18m\)
- Right Side: \(6m^2(1 + 3m) = 6m^2 \cdot 1 + 6m^2 \cdot 3m = 6m^2 + 18m\)

**Result**: Left Side is equal to Right Side. **True**.

3. **Statement**: \(32m^4 + 12m^3 = 4m^3(8m + 3)\)

**Evaluation**:
- Left Side: \(32m^4 + 12m^3\)
- Right Side: \(4m^3(8m + 3) = 4m^3 \cdot 8m + 4m^3 \cdot 3 = 32m^4 + 12m^3\)

**Result**: Left Side is equal to Right Side. **True**.

4. **Statement**: \(40m^6 - 4 = 4(10m^6 - 1)\)

**Evaluation**:
- Left Side: \(40m^6 - 4\)
- Right Side: \(4(10m^6 - 1) = 4 \cdot 10m^6 - 4 \cdot 1 = 40m^6 - 4\)

**Result**: Left Side is equal to Right Side. **True**.

**Final Result**: The true statements are:

- \(6m^2 + 18m = 6m^2(1 + 3m)\)
- \(32m^4 + 12m^3 = 4m^3(8m + 3)\)
- \(40m^6 - 4 = 4(10m^6 - 1)\)