Question
Answer
$$(2x^2+3x-4)(2x^2-3x+4)=4x^4-9x^2+24x-16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x^2+3x-4)(2x^2-3x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^4-9x^2+24x-16\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x^2+3x-4}\right) $ by each term in $ \left( 2x^2-3x+4\right) $. $$ \left( \color{blue}{2x^2+3x-4}\right) \cdot \left( 2x^2-3x+4\right) = \\ = 4x^4 -\cancel{6x^3}+ \cancel{8x^2}+ \cancel{6x^3}-9x^2+12x -\cancel{8x^2}+12x-16 $$ |
| ② | Combine like terms: $$ 4x^4 \, \color{blue}{ -\cancel{6x^3}} \,+ \, \color{green}{ \cancel{8x^2}} \,+ \, \color{blue}{ \cancel{6x^3}} \, \color{blue}{-9x^2} + \color{red}{12x} \, \color{blue}{ -\cancel{8x^2}} \,+ \color{red}{12x} -16 = 4x^4 \color{blue}{-9x^2} + \color{red}{24x} -16 $$ |
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