Tap the blue circles to see an explanation.
$$ \begin{aligned}(x-\frac{1}{2})^3+9(x-\frac{1}{2})^2+28(x-\frac{1}{2})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x-\frac{1}{2})^3+9(x-\frac{1}{2})^2+28\frac{2x-1}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x-\frac{1}{2})^3+9(x-\frac{1}{2})^2+\frac{56x-28}{2}\end{aligned} $$ | |
① | Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract raitonal expressions, both fractions must have the same denominator. |
② | Step 1: Write $ 28 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 28 \cdot \frac{2x-1}{2} & \xlongequal{\text{Step 1}} \frac{28}{\color{red}{1}} \cdot \frac{2x-1}{2} \xlongequal{\text{Step 2}} \frac{ 28 \cdot \left( 2x-1 \right) }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 56x-28 }{ 2 } \end{aligned} $$ |