Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

◀ back to index

Question

Answer

$$x^3-\dfrac{32}{2}x^2+72x-\dfrac{193}{2}=\dfrac{2x^3-32x^2+144x-193}{2}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}x^3-\frac{32}{2}x^2+72x-\frac{193}{2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^3 - \frac{ 32 : \color{orangered}{ 2 } }{ 2 : \color{orangered}{ 2 }} \cdot x^2 + 72x - \frac{193}{2} \xlongequal{ } \\[1 em] & \xlongequal{ }x^3-\frac{16}{1}x^2+72x-\frac{193}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3-16x^2+72x-\frac{193}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2x^3-32x^2+144x-193}{2}\end{aligned} $$
①
Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $.
②
Remove 1 from denominator.
③

Subtract $ \dfrac{193}{2} $ from $ x^3-16x^2+72x $ to get $ \dfrac{ \color{purple}{ 2x^3-32x^2+144x-193 } }{ 2 }$.

Step 1: Write $ x^3-16x^2+72x $ 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 $\color{blue}{ 2 }$.

$$ \begin{aligned} x^3-16x^2+72x- \frac{193}{2} & \xlongequal{\text{Step 1}} \frac{x^3-16x^2+72x}{\color{red}{1}} - \frac{193}{2} = \frac{ \left( x^3-16x^2+72x \right) \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} - \frac{ 193 }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2x^3-32x^2+144x } }{ 2 } - \frac{ \color{purple}{ 193 } }{ 2 }=\frac{ \color{purple}{ 2x^3-32x^2+144x-193 } }{ 2 } \end{aligned} $$
This page was created using
Simplify polynomials calculator