Question
Answer
$$(2x-5)(2x-1)(x^2+1)=4x^4-12x^3+9x^2-12x+5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x-5)(2x-1)(x^2+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4x^2-2x-10x+5)(x^2+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(4x^2-12x+5)(x^2+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^4+4x^2-12x^3-12x+5x^2+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4x^4-12x^3+9x^2-12x+5\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x-5}\right) $ by each term in $ \left( 2x-1\right) $. $$ \left( \color{blue}{2x-5}\right) \cdot \left( 2x-1\right) = 4x^2-2x-10x+5 $$ |
| ② | Combine like terms: $$ 4x^2 \color{blue}{-2x} \color{blue}{-10x} +5 = 4x^2 \color{blue}{-12x} +5 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{4x^2-12x+5}\right) $ by each term in $ \left( x^2+1\right) $. $$ \left( \color{blue}{4x^2-12x+5}\right) \cdot \left( x^2+1\right) = 4x^4+4x^2-12x^3-12x+5x^2+5 $$ |
| ④ | Combine like terms: $$ 4x^4+ \color{blue}{4x^2} -12x^3-12x+ \color{blue}{5x^2} +5 = 4x^4-12x^3+ \color{blue}{9x^2} -12x+5 $$ |
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