Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+13)(x+11)(x+6)(x-3)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x+13)(x+11)(x+6)(x^2-6x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+11x+13x+143)(x+6)(x^2-6x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^2+24x+143)(x+6)(x^2-6x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3+6x^2+24x^2+144x+143x+858)(x^2-6x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}(x^3+30x^2+287x+858)(x^2-6x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}x^5+24x^4+116x^3-594x^2-2565x+7722\end{aligned} $$ | |
| ① | Find $ \left(x-3\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 3 }$. $$ \begin{aligned}\left(x-3\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 3 + \color{red}{3^2} = x^2-6x+9\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x+13}\right) $ by each term in $ \left( x+11\right) $. $$ \left( \color{blue}{x+13}\right) \cdot \left( x+11\right) = x^2+11x+13x+143 $$ |
| ③ | Combine like terms: $$ x^2+ \color{blue}{11x} + \color{blue}{13x} +143 = x^2+ \color{blue}{24x} +143 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{x^2+24x+143}\right) $ by each term in $ \left( x+6\right) $. $$ \left( \color{blue}{x^2+24x+143}\right) \cdot \left( x+6\right) = x^3+6x^2+24x^2+144x+143x+858 $$ |
| ⑤ | Combine like terms: $$ x^3+ \color{blue}{6x^2} + \color{blue}{24x^2} + \color{red}{144x} + \color{red}{143x} +858 = x^3+ \color{blue}{30x^2} + \color{red}{287x} +858 $$ |
| ⑥ | Multiply each term of $ \left( \color{blue}{x^3+30x^2+287x+858}\right) $ by each term in $ \left( x^2-6x+9\right) $. $$ \left( \color{blue}{x^3+30x^2+287x+858}\right) \cdot \left( x^2-6x+9\right) = \\ = x^5-6x^4+9x^3+30x^4-180x^3+270x^2+287x^3-1722x^2+2583x+858x^2-5148x+7722 $$ |
| ⑦ | Combine like terms: $$ x^5 \color{blue}{-6x^4} + \color{red}{9x^3} + \color{blue}{30x^4} \color{green}{-180x^3} + \color{orange}{270x^2} + \color{green}{287x^3} \color{blue}{-1722x^2} + \color{red}{2583x} + \color{blue}{858x^2} \color{red}{-5148x} +7722 = \\ = x^5+ \color{blue}{24x^4} + \color{green}{116x^3} \color{blue}{-594x^2} \color{red}{-2565x} +7722 $$ |