Question
Answer
$$\dfrac{55-3x}{2}\cdot(26-2x)x=\dfrac{6x^3-188x^2+1430x}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{55-3x}{2}\cdot(26-2x)x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6x^2-188x+1430}{2}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6x^3-188x^2+1430x}{2}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{55-3x}{2} $ by $ 26-2x $ to get $ \dfrac{6x^2-188x+1430}{2} $. Step 1: Write $ 26-2x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{55-3x}{2} \cdot 26-2x & \xlongequal{\text{Step 1}} \frac{55-3x}{2} \cdot \frac{26-2x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 55-3x \right) \cdot \left( 26-2x \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1430-110x-78x+6x^2 }{ 2 } = \frac{6x^2-188x+1430}{2} \end{aligned} $$ |
| ② | Multiply $ \dfrac{6x^2-188x+1430}{2} $ by $ x $ to get $ \dfrac{ 6x^3-188x^2+1430x }{ 2 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{6x^2-188x+1430}{2} \cdot x & \xlongequal{\text{Step 1}} \frac{6x^2-188x+1430}{2} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 6x^2-188x+1430 \right) \cdot x }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6x^3-188x^2+1430x }{ 2 } \end{aligned} $$ |
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