$$(\dfrac{7}{4}a^2-3)(\dfrac{7}{4}a^2+3)=\dfrac{49a^4-144}{16}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(\frac{7}{4}a^2-3)(\frac{7}{4}a^2+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(\frac{7a^2}{4}-3)(\frac{7a^2}{4}+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{7a^2-12}{4}\frac{7a^2+12}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{49a^4-144}{16}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{7}{4} $ by $ a^2 $ to get $ \dfrac{ 7a^2 }{ 4 } $. 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. $$ \begin{aligned} \frac{7}{4} \cdot a^2 & \xlongequal{\text{Step 1}} \frac{7}{4} \cdot \frac{a^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7 \cdot a^2 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7a^2 }{ 4 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{7}{4} $ by $ a^2 $ to get $ \dfrac{ 7a^2 }{ 4 } $. 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. $$ \begin{aligned} \frac{7}{4} \cdot a^2 & \xlongequal{\text{Step 1}} \frac{7}{4} \cdot \frac{a^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7 \cdot a^2 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7a^2 }{ 4 } \end{aligned} $$ |
| ③ | Subtract $3$ from $ \dfrac{7a^2}{4} $ to get $ \dfrac{ \color{purple}{ 7a^2-12 } }{ 4 }$. Step 1: Write $ 3 $ 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{7a^2}{4} $ and $ 3 $ to get $ \dfrac{ \color{purple}{ 7a^2+12 } }{ 4 }$. Step 1: Write $ 3 $ 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{7a^2-12}{4} $ by $ \dfrac{7a^2+12}{4} $ to get $ \dfrac{49a^4-144}{16} $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{7a^2-12}{4} \cdot \frac{7a^2+12}{4} & \xlongequal{\text{Step 1}} \frac{ \left( 7a^2-12 \right) \cdot \left( 7a^2+12 \right) }{ 4 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 49a^4+ \cancel{84a^2} -\cancel{84a^2}-144 }{ 16 } = \frac{49a^4-144}{16} \end{aligned} $$ |