Question
Answer
$$(x+1)(x+3)(x-4)=x^3-13x-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+1)(x+3)(x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+3x+x+3)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+4x+3)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-4x^2+4x^2-16x+3x-12 \xlongequal{ } \\[1 em] & \xlongequal{ }x^3 -\cancel{4x^2}+ \cancel{4x^2}-16x+3x-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-13x-12\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+1}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x+1}\right) \cdot \left( x+3\right) = x^2+3x+x+3 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{3x} + \color{blue}{x} +3 = x^2+ \color{blue}{4x} +3 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+4x+3}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x^2+4x+3}\right) \cdot \left( x-4\right) = x^3 -\cancel{4x^2}+ \cancel{4x^2}-16x+3x-12 $$ |
| ④ | Combine like terms: $$ x^3 \, \color{blue}{ -\cancel{4x^2}} \,+ \, \color{blue}{ \cancel{4x^2}} \, \color{green}{-16x} + \color{green}{3x} -12 = x^3 \color{green}{-13x} -12 $$ |
This page was created using
Simplify polynomials calculator