Answer
$$\frac{1}{2}(4x-y)(4x+y)=\frac{16x^2-y^2}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{2}(4x-y)(4x+y)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4x-y}{2}(4x+y) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{16x^2-y^2}{2}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{1}{2} $ by $ 4x-y $ to get $ \dfrac{ 4x-y }{ 2 } $. Step 1: Write $ 4x-y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{2} \cdot 4x-y & \xlongequal{\text{Step 1}} \frac{1}{2} \cdot \frac{4x-y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( 4x-y \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x-y }{ 2 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{4x-y}{2} $ by $ 4x+y $ to get $ \dfrac{16x^2-y^2}{2} $. Step 1: Write $ 4x+y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x-y}{2} \cdot 4x+y & \xlongequal{\text{Step 1}} \frac{4x-y}{2} \cdot \frac{4x+y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 4x-y \right) \cdot \left( 4x+y \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 16x^2+ \cancel{4xy} -\cancel{4xy}-y^2 }{ 2 } = \frac{16x^2-y^2}{2} \end{aligned} $$ |
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