Question
Answer
$$9(x-3)^2(x^2+6)=9x^4-54x^3+135x^2-324x+486$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}9(x-3)^2(x^2+6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9(x^2-6x+9)(x^2+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(9x^2-54x+81)(x^2+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}9x^4+54x^2-54x^3-324x+81x^2+486 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}9x^4-54x^3+135x^2-324x+486\end{aligned} $$ | |
| 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 $ \color{blue}{9} $ by $ \left( x^2-6x+9\right) $ $$ \color{blue}{9} \cdot \left( x^2-6x+9\right) = 9x^2-54x+81 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{9x^2-54x+81}\right) $ by each term in $ \left( x^2+6\right) $. $$ \left( \color{blue}{9x^2-54x+81}\right) \cdot \left( x^2+6\right) = 9x^4+54x^2-54x^3-324x+81x^2+486 $$ |
| ④ | Combine like terms: $$ 9x^4+ \color{blue}{54x^2} -54x^3-324x+ \color{blue}{81x^2} +486 = 9x^4-54x^3+ \color{blue}{135x^2} -324x+486 $$ |
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