Question
Answer
$$(x-4)(x+3)(x+1)=x^3-13x-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-4)(x+3)(x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+3x-4x-12)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-x-12)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+x^2-x^2-x-12x-12 \xlongequal{ } \\[1 em] & \xlongequal{ }x^3+ \cancel{x^2} -\cancel{x^2}-x-12x-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-13x-12\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-4}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x-4}\right) \cdot \left( x+3\right) = x^2+3x-4x-12 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{3x} \color{blue}{-4x} -12 = x^2 \color{blue}{-x} -12 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-x-12}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x^2-x-12}\right) \cdot \left( x+1\right) = x^3+ \cancel{x^2} -\cancel{x^2}-x-12x-12 $$ |
| ④ | Combine like terms: $$ x^3+ \, \color{blue}{ \cancel{x^2}} \, \, \color{blue}{ -\cancel{x^2}} \, \color{green}{-x} \color{green}{-12x} -12 = x^3 \color{green}{-13x} -12 $$ |
This page was created using
Simplify polynomials calculator