Question
Answer
$$(x+2.51818)(x+2.51818)(x-1.8289)(x-1.8289)=x^4+2x^3-3x^2-4x+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2.51818)(x+2.51818)(x-1.8289)(x-1.8289)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x+2x+4)(x-1.8289)(x-1.8289) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+4x+4)(x-1.8289)(x-1.8289) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3-x^2+4x^2-4x+4x-4)(x-1.8289) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3+3x^2-4)(x-1.8289) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}x^4-x^3+3x^3-3x^2-4x+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^4+2x^3-3x^2-4x+4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+2}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x+2}\right) \cdot \left( x+2\right) = x^2+2x+2x+4 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{2x} + \color{blue}{2x} +4 = x^2+ \color{blue}{4x} +4 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+4x+4}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{x^2+4x+4}\right) \cdot \left( x-1\right) = x^3-x^2+4x^2 -\cancel{4x}+ \cancel{4x}-4 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-x^2} + \color{blue}{4x^2} \, \color{red}{ -\cancel{4x}} \,+ \, \color{red}{ \cancel{4x}} \,-4 = x^3+ \color{blue}{3x^2} -4 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3+3x^2-4}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{x^3+3x^2-4}\right) \cdot \left( x-1\right) = x^4-x^3+3x^3-3x^2-4x+4 $$ |
| ⑥ | Combine like terms: $$ x^4 \color{blue}{-x^3} + \color{blue}{3x^3} -3x^2-4x+4 = x^4+ \color{blue}{2x^3} -3x^2-4x+4 $$ |
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