Question
Answer
$$\dfrac{1}{2}w(14w^3+18w^2+10w-6)=\dfrac{14w^4+18w^3+10w^2-6w}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{2}w(14w^3+18w^2+10w-6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{w}{2}(14w^3+18w^2+10w-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{14w^4+18w^3+10w^2-6w}{2}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{1}{2} $ by $ w $ to get $ \dfrac{ w }{ 2 } $. Step 1: Write $ w $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{2} \cdot w & \xlongequal{\text{Step 1}} \frac{1}{2} \cdot \frac{w}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot w }{ 2 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ w }{ 2 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{w}{2} $ by $ 14w^3+18w^2+10w-6 $ to get $ \dfrac{ 14w^4+18w^3+10w^2-6w }{ 2 } $. Step 1: Write $ 14w^3+18w^2+10w-6 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{w}{2} \cdot 14w^3+18w^2+10w-6 & \xlongequal{\text{Step 1}} \frac{w}{2} \cdot \frac{14w^3+18w^2+10w-6}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ w \cdot \left( 14w^3+18w^2+10w-6 \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 14w^4+18w^3+10w^2-6w }{ 2 } \end{aligned} $$ |
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