Question
Answer
$$(x+3)(x+1)(x+5)(x+6)=x^4+15x^3+77x^2+153x+90$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+3)(x+1)(x+5)(x+6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+x+3x+3)(x+5)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+4x+3)(x+5)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3+5x^2+4x^2+20x+3x+15)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3+9x^2+23x+15)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^4+15x^3+77x^2+153x+90\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+3}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x+3}\right) \cdot \left( x+1\right) = x^2+x+3x+3 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{x} + \color{blue}{3x} +3 = x^2+ \color{blue}{4x} +3 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+4x+3}\right) $ by each term in $ \left( x+5\right) $. $$ \left( \color{blue}{x^2+4x+3}\right) \cdot \left( x+5\right) = x^3+5x^2+4x^2+20x+3x+15 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{5x^2} + \color{blue}{4x^2} + \color{red}{20x} + \color{red}{3x} +15 = x^3+ \color{blue}{9x^2} + \color{red}{23x} +15 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3+9x^2+23x+15}\right) $ by each term in $ \left( x+6\right) $. $$ \left( \color{blue}{x^3+9x^2+23x+15}\right) \cdot \left( x+6\right) = x^4+6x^3+9x^3+54x^2+23x^2+138x+15x+90 $$ |
| ⑥ | Combine like terms: $$ x^4+ \color{blue}{6x^3} + \color{blue}{9x^3} + \color{red}{54x^2} + \color{red}{23x^2} + \color{green}{138x} + \color{green}{15x} +90 = \\ = x^4+ \color{blue}{15x^3} + \color{red}{77x^2} + \color{green}{153x} +90 $$ |
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