$$63\cdot(9-\dfrac{9}{7}x)-9x\cdot(9-\dfrac{9}{7}x)-\dfrac{7}{2}(9-\dfrac{9}{7}x)^2=\dfrac{81x^2-1134x+3969}{7}-\dfrac{7}{2}(9-\dfrac{9}{7}x)^2$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}63\cdot(9-\frac{9}{7}x)-9x\cdot(9-\frac{9}{7}x)-\frac{7}{2}(9-\frac{9}{7}x)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(63-9x)\cdot(9-\frac{9}{7}x)-\frac{7}{2}(9-\frac{9}{7}x)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(63-9x)\cdot(9-\frac{9x}{7})-\frac{7}{2}(9-\frac{9}{7}x)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(63-9x)\frac{-9x+63}{7}-\frac{7}{2}(9-\frac{9}{7}x)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{81x^2-1134x+3969}{7}-\frac{7}{2}(9-\frac{9}{7}x)^2\end{aligned} $$ | |
| ① | Use the distributive property. |
| ② | Multiply $ \dfrac{9}{7} $ by $ x $ to get $ \dfrac{ 9x }{ 7 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{9}{7} \cdot x & \xlongequal{\text{Step 1}} \frac{9}{7} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9 \cdot x }{ 7 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 9x }{ 7 } \end{aligned} $$ |
| ③ | Subtract $ \dfrac{9x}{7} $ from $ 9 $ to get $ \dfrac{ \color{purple}{ -9x+63 } }{ 7 }$. Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract raitonal expressions, both fractions must have the same denominator. |
| ④ | Multiply $63-9x$ by $ \dfrac{-9x+63}{7} $ to get $ \dfrac{81x^2-1134x+3969}{7} $. Step 1: Write $ 63-9x $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 63-9x \cdot \frac{-9x+63}{7} & \xlongequal{\text{Step 1}} \frac{63-9x}{\color{red}{1}} \cdot \frac{-9x+63}{7} \xlongequal{\text{Step 2}} \frac{ \left( 63-9x \right) \cdot \left( -9x+63 \right) }{ 1 \cdot 7 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -567x+3969+81x^2-567x }{ 7 } = \frac{81x^2-1134x+3969}{7} \end{aligned} $$ |