Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-8k-12)(\frac{1}{4}k+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-8k-12)(\frac{k}{4}+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(-8k-12)\frac{k+12}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-8k^2-108k-144}{4}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{1}{4} $ by $ k $ to get $ \dfrac{ k }{ 4 } $. Step 1: Write $ k $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{4} \cdot k & \xlongequal{\text{Step 1}} \frac{1}{4} \cdot \frac{k}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot k }{ 4 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ k }{ 4 } \end{aligned} $$ |
| ② | Add $ \dfrac{k}{4} $ and $ 3 $ to get $ \dfrac{ \color{purple}{ k+12 } }{ 4 }$. Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To add raitonal expressions, both fractions must have the same denominator. |
| ③ | Multiply $-8k-12$ by $ \dfrac{k+12}{4} $ to get $ \dfrac{-8k^2-108k-144}{4} $. Step 1: Write $ -8k-12 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} -8k-12 \cdot \frac{k+12}{4} & \xlongequal{\text{Step 1}} \frac{-8k-12}{\color{red}{1}} \cdot \frac{k+12}{4} \xlongequal{\text{Step 2}} \frac{ \left( -8k-12 \right) \cdot \left( k+12 \right) }{ 1 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -8k^2-96k-12k-144 }{ 4 } = \frac{-8k^2-108k-144}{4} \end{aligned} $$ |