$$6\cdot\dfrac{x}{4}x-16(x-4)\dfrac{x+4}{4}=\dfrac{-10x^2+256}{4}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6 \cdot \frac{x}{4}x-16(x-4)\frac{x+4}{4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6 \cdot \frac{x}{4}x-(16x-64)\frac{x+4}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6x}{4}x-\frac{16x^2-256}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{6x^2}{4}-\frac{16x^2-256}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{-10x^2+256}{4}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{16} $ by $ \left( x-4\right) $ $$ \color{blue}{16} \cdot \left( x-4\right) = 16x-64 $$ |
| ② | Multiply $6$ by $ \dfrac{x}{4} $ to get $ \dfrac{ 6x }{ 4 } $. Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 6 \cdot \frac{x}{4} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} \cdot \frac{x}{4} \xlongequal{\text{Step 2}} \frac{ 6 \cdot x }{ 1 \cdot 4 } \xlongequal{\text{Step 3}} \frac{ 6x }{ 4 } \end{aligned} $$ |
| ③ | Multiply $16x-64$ by $ \dfrac{x+4}{4} $ to get $ \dfrac{16x^2-256}{4} $. Step 1: Write $ 16x-64 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 16x-64 \cdot \frac{x+4}{4} & \xlongequal{\text{Step 1}} \frac{16x-64}{\color{red}{1}} \cdot \frac{x+4}{4} \xlongequal{\text{Step 2}} \frac{ \left( 16x-64 \right) \cdot \left( x+4 \right) }{ 1 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 16x^2+ \cancel{64x} -\cancel{64x}-256 }{ 4 } = \frac{16x^2-256}{4} \end{aligned} $$ |
| ④ | Multiply $ \dfrac{6x}{4} $ by $ x $ to get $ \dfrac{ 6x^2 }{ 4 } $. 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. $$ \begin{aligned} \frac{6x}{4} \cdot x & \xlongequal{\text{Step 1}} \frac{6x}{4} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 6x \cdot x }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6x^2 }{ 4 } \end{aligned} $$ |
| ⑤ | Multiply $16x-64$ by $ \dfrac{x+4}{4} $ to get $ \dfrac{16x^2-256}{4} $. Step 1: Write $ 16x-64 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 16x-64 \cdot \frac{x+4}{4} & \xlongequal{\text{Step 1}} \frac{16x-64}{\color{red}{1}} \cdot \frac{x+4}{4} \xlongequal{\text{Step 2}} \frac{ \left( 16x-64 \right) \cdot \left( x+4 \right) }{ 1 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 16x^2+ \cancel{64x} -\cancel{64x}-256 }{ 4 } = \frac{16x^2-256}{4} \end{aligned} $$ |
| ⑥ | Subtract $ \dfrac{16x^2-256}{4} $ from $ \dfrac{6x^2}{4} $ to get $ \dfrac{-10x^2+256}{4} $. To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{6x^2}{4} - \frac{16x^2-256}{4} & = \frac{6x^2}{\color{blue}{4}} - \frac{16x^2-256}{\color{blue}{4}} = \\[1ex] &=\frac{ 6x^2 - \left( 16x^2-256 \right) }{ \color{blue}{ 4 }}= \frac{-10x^2+256}{4} \end{aligned} $$ |