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