Question
Answer
$$(2x^2-3x+4)(5x^2+2x-1)=10x^4-11x^3+12x^2+11x-4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x^2-3x+4)(5x^2+2x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}10x^4-11x^3+12x^2+11x-4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x^2-3x+4}\right) $ by each term in $ \left( 5x^2+2x-1\right) $. $$ \left( \color{blue}{2x^2-3x+4}\right) \cdot \left( 5x^2+2x-1\right) = 10x^4+4x^3-2x^2-15x^3-6x^2+3x+20x^2+8x-4 $$ |
| ② | Combine like terms: $$ 10x^4+ \color{blue}{4x^3} \color{red}{-2x^2} \color{blue}{-15x^3} \color{green}{-6x^2} + \color{orange}{3x} + \color{green}{20x^2} + \color{orange}{8x} -4 = \\ = 10x^4 \color{blue}{-11x^3} + \color{green}{12x^2} + \color{orange}{11x} -4 $$ |
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