Question
Answer
$$9(3+x)^3-1\cdot(3+x)+8=9x^3+81x^2+242x+248$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}9(3+x)^3-1\cdot(3+x)+8& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9(27+27x+9x^2+x^3)-1\cdot(3+x)+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}243+243x+81x^2+9x^3-(3+x)+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}243+243x+81x^2+9x^3-3-x+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}9x^3+81x^2+242x+248\end{aligned} $$ | |
| ① | Find $ \left(3+x\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 3 $ and $ B = x $. $$ \left(3+x\right)^3 = 3^3+3 \cdot 3^2 \cdot x + 3 \cdot 3 \cdot x^2+x^3 = 27+27x+9x^2+x^3 $$ |
| ② | Multiply $ \color{blue}{9} $ by $ \left( 27+27x+9x^2+x^3\right) $ $$ \color{blue}{9} \cdot \left( 27+27x+9x^2+x^3\right) = 243+243x+81x^2+9x^3 $$Multiply $ \color{blue}{1} $ by $ \left( 3+x\right) $ $$ \color{blue}{1} \cdot \left( 3+x\right) = 3+x $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 3+x \right) = -3-x $$ |
| ④ | Combine like terms: $$ \color{blue}{243} + \color{red}{243x} +81x^2+9x^3 \color{green}{-3} \color{red}{-x} + \color{green}{8} = 9x^3+81x^2+ \color{red}{242x} + \color{green}{248} $$ |
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