Question

Factor 8mn2 + 12mn completely. A 42mn’ +3mn) B 4mn(2 + 3n) C 4mn(2mn + 3) D 4mn(2n + 3)

Answer 1

Question 1Step 1: Problem

`\text{Factor 8mn}^2\text{ + 12mn}`

Step 2: Concept

Factor the highest common factor out.

Step 3: Method

`8mn^2\text{ + 12mn = 4mn( 2n + 3)}`

Step 4: Final answer

4mn(2n + 3)

Question 2

Step 1: Question

`\text{Simplify }\frac{(1.24\text{ }*10^2\text{ ) (3.6 }*10^(-3))}{1.8\text{ }*\text{ 10}}`

Step 2: Concept

Apply laws of exponent

`\begin{gathered} \text{Division law } \\ (m^x)/(m^y)=m^{x\text{ - y}}^{} \\ \text{Multiplication law} \\ m^x\text{ }* m^y=m^{x\text{ + y}} \end{gathered}`

Step 3: Method

`\begin{gathered} =\text{ }\frac{(1.24\text{ }*10^2\text{ )(3.6 }*10^(-3))}{1.8\text{ x 10}} \\ =\text{ }\frac{1.24\text{ }*\text{ 3.6 }*10^{2\text{ + (-3)}}}{18} \\ =\text{ }\frac{4.464\text{ }*10^{2\text{ - 3}}}{18} \\ =\text{ }\frac{4.464\text{ }*10^(-1)}{18} \\ =\text{ }(4.464)/(18)\text{ }*10^(-1) \\ =\text{ 0.248 }*10^(-1) \\ =\text{ 2.48 }*10^(-2) \end{gathered}`

Step 4: Final answer

Option D is the correct answer

`2.48\text{ }*10^(-2)`