Question
Answer
$$x^2(3x^2+4x-2)+x(x^2-3x+1)=3x^4+5x^3-5x^2+x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x^2(3x^2+4x-2)+x(x^2-3x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3x^4+4x^3-2x^2+x^3-3x^2+x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x^4+5x^3-5x^2+x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{x^2} $ by $ \left( 3x^2+4x-2\right) $ $$ \color{blue}{x^2} \cdot \left( 3x^2+4x-2\right) = 3x^4+4x^3-2x^2 $$Multiply $ \color{blue}{x} $ by $ \left( x^2-3x+1\right) $ $$ \color{blue}{x} \cdot \left( x^2-3x+1\right) = x^3-3x^2+x $$ |
| ② | Combine like terms: $$ 3x^4+ \color{blue}{4x^3} \color{red}{-2x^2} + \color{blue}{x^3} \color{red}{-3x^2} +x = 3x^4+ \color{blue}{5x^3} \color{red}{-5x^2} +x $$ |
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