$$(\dfrac{3}{7}a^2-8)(\dfrac{3}{7}a^2+8)=\dfrac{9a^4-3136}{49}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(\frac{3}{7}a^2-8)(\frac{3}{7}a^2+8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(\frac{3a^2}{7}-8)(\frac{3a^2}{7}+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{3a^2-56}{7}\frac{3a^2+56}{7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{9a^4-3136}{49}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{3}{7} $ by $ a^2 $ to get $ \dfrac{ 3a^2 }{ 7 } $. Step 1: Write $ a^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{3}{7} \cdot a^2 & \xlongequal{\text{Step 1}} \frac{3}{7} \cdot \frac{a^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot a^2 }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3a^2 }{ 7 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{3}{7} $ by $ a^2 $ to get $ \dfrac{ 3a^2 }{ 7 } $. Step 1: Write $ a^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{3}{7} \cdot a^2 & \xlongequal{\text{Step 1}} \frac{3}{7} \cdot \frac{a^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot a^2 }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3a^2 }{ 7 } \end{aligned} $$ |
| ③ | Subtract $8$ from $ \dfrac{3a^2}{7} $ to get $ \dfrac{ \color{purple}{ 3a^2-56 } }{ 7 }$. Step 1: Write $ 8 $ 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 | Add $ \dfrac{3a^2}{7} $ and $ 8 $ to get $ \dfrac{ \color{purple}{ 3a^2+56 } }{ 7 }$. Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To add raitonal expressions, both fractions must have the same denominator. |
| ⑤ | Multiply $ \dfrac{3a^2-56}{7} $ by $ \dfrac{3a^2+56}{7} $ to get $ \dfrac{9a^4-3136}{49} $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{3a^2-56}{7} \cdot \frac{3a^2+56}{7} & \xlongequal{\text{Step 1}} \frac{ \left( 3a^2-56 \right) \cdot \left( 3a^2+56 \right) }{ 7 \cdot 7 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 9a^4+ \cancel{168a^2} -\cancel{168a^2}-3136 }{ 49 } = \frac{9a^4-3136}{49} \end{aligned} $$ |