Answer
$$7x^3+21\cdot\frac{x^2}{21}x=8x^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7x^3+21 \cdot \frac{x^2}{21}x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}7x^3+x^2x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}7x^3+x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8x^3\end{aligned} $$ | |
| ① | Multiply $21$ by $ \dfrac{x^2}{21} $ to get $ x^2$. Step 1: Write $ 21 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Cancel $ \color{blue}{ 21 } $ in first and second fraction. Step 3: Multiply numerators and denominators. Step 4: Simplify numerator and denominator. $$ \begin{aligned} 21 \cdot \frac{x^2}{21} & \xlongequal{\text{Step 1}} \frac{21}{\color{red}{1}} \cdot \frac{x^2}{21} \xlongequal{\text{Step 2}} \frac{\color{blue}{1}}{1} \cdot \frac{x^2}{\color{blue}{1}} = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1 \cdot x^2 }{ 1 \cdot 1 } \xlongequal{\text{Step 4}} \frac{ x^2 }{ 1 } =x^2 \end{aligned} $$ |
| ② | $$ 1 x^2 x = x^{2 + 1} = x^3 $$ |
| ③ | Combine like terms: $$ \color{blue}{7x^3} + \color{blue}{x^3} = \color{blue}{8x^3} $$ |
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