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Question

Answer

$$(4x-\dfrac{1}{6})(4x+\dfrac{1}{6})=\dfrac{576x^2-1}{36}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}(4x-\frac{1}{6})(4x+\frac{1}{6})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24x-1}{6}\frac{24x+1}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{576x^2-1}{36}\end{aligned} $$
①

Subtract $ \dfrac{1}{6} $ from $ 4x $ to get $ \dfrac{ \color{purple}{ 24x-1 } }{ 6 }$.

Step 1: Write $ 4x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 6 }$.

$$ \begin{aligned} 4x- \frac{1}{6} & \xlongequal{\text{Step 1}} \frac{4x}{\color{red}{1}} - \frac{1}{6} = \frac{ 4x \cdot \color{blue}{ 6 }}{ 1 \cdot \color{blue}{ 6 }} - \frac{ 1 }{ 6 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 24x } }{ 6 } - \frac{ \color{purple}{ 1 } }{ 6 }=\frac{ \color{purple}{ 24x-1 } }{ 6 } \end{aligned} $$
②

Add $4x$ and $ \dfrac{1}{6} $ to get $ \dfrac{ \color{purple}{ 24x+1 } }{ 6 }$.

Step 1: Write $ 4x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 6 }$.

$$ \begin{aligned} 4x+ \frac{1}{6} & \xlongequal{\text{Step 1}} \frac{4x}{\color{red}{1}} + \frac{1}{6} = \frac{ 4x \cdot \color{blue}{ 6 }}{ 1 \cdot \color{blue}{ 6 }} + \frac{ 1 }{ 6 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 24x } }{ 6 } + \frac{ \color{purple}{ 1 } }{ 6 }=\frac{ \color{purple}{ 24x+1 } }{ 6 } \end{aligned} $$
③

Multiply $ \dfrac{24x-1}{6} $ by $ \dfrac{24x+1}{6} $ to get $ \dfrac{576x^2-1}{36} $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{24x-1}{6} \cdot \frac{24x+1}{6} & \xlongequal{\text{Step 1}} \frac{ \left( 24x-1 \right) \cdot \left( 24x+1 \right) }{ 6 \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 576x^2+ \cancel{24x} -\cancel{24x}-1 }{ 36 } = \frac{576x^2-1}{36} \end{aligned} $$
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