$$(a-\dfrac{1}{5}y)(a+\dfrac{1}{5}y)=\dfrac{25a^2-y^2}{25}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a-\frac{1}{5}y)(a+\frac{1}{5}y)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(a-\frac{y}{5})(a+\frac{y}{5}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{5a-y}{5}\frac{5a+y}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{25a^2-y^2}{25}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{1}{5} $ by $ y $ to get $ \dfrac{ y }{ 5 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{1}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot y }{ 5 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ y }{ 5 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{1}{5} $ by $ y $ to get $ \dfrac{ y }{ 5 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{1}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot y }{ 5 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ y }{ 5 } \end{aligned} $$ |
| ③ | Subtract $ \dfrac{y}{5} $ from $ a $ to get $ \dfrac{ \color{purple}{ 5a-y } }{ 5 }$. Step 1: Write $ a $ 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 $a$ and $ \dfrac{y}{5} $ to get $ \dfrac{ \color{purple}{ 5a+y } }{ 5 }$. Step 1: Write $ a $ 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{5a-y}{5} $ by $ \dfrac{5a+y}{5} $ to get $ \dfrac{25a^2-y^2}{25} $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{5a-y}{5} \cdot \frac{5a+y}{5} & \xlongequal{\text{Step 1}} \frac{ \left( 5a-y \right) \cdot \left( 5a+y \right) }{ 5 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 25a^2+ \cancel{5ay} -\cancel{5ay}-y^2 }{ 25 } = \frac{25a^2-y^2}{25} \end{aligned} $$ |