Tap the blue circles to see an explanation.
| $$ \begin{aligned}5v^2-5 \cdot \frac{v}{1}-v& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(v^2-\frac{v}{1})\cdot5-v \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{v^2-v}{1}\cdot5-v \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5v^2-5v-v \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}5v^2-6v\end{aligned} $$ | |
| ① | Use the distributive property. |
| ② | Subtract $ \dfrac{v}{1} $ from $ v^2 $ to get $ \dfrac{ v^2 - v }{ \color{blue}{ 1 }}$. Step 1: Write $ v^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator. $$ \begin{aligned} v^2- \frac{v}{1} & \xlongequal{\text{Step 1}} \frac{v^2}{\color{red}{1}} - \frac{v}{1} \xlongequal{\text{Step 2}} \frac{v^2}{\color{blue}{1}} - \frac{v}{\color{blue}{1}} = \\[1ex] &=\frac{ v^2 - v }{ \color{blue}{ 1 }} \end{aligned} $$ |
| ③ | Multiply $ \dfrac{v^2-v}{1} $ by $ 5 $ to get $ 5v^2-5v$. Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{v^2-v}{1} \cdot 5 & \xlongequal{\text{Step 1}} \frac{v^2-v}{1} \cdot \frac{5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( v^2-v \right) \cdot 5 }{ 1 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5v^2-5v }{ 1 } =5v^2-5v \end{aligned} $$ |
| ④ | Combine like terms: $$ 5v^2 \color{blue}{-5v} \color{blue}{-v} = 5v^2 \color{blue}{-6v} $$ |