Answer
$$1+(3x+5)^3=27x^3+135x^2+225x+126$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}1+(3x+5)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}1+27x^3+135x^2+225x+125 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}27x^3+135x^2+225x+126\end{aligned} $$ | |
| ① | Find $ \left(3x+5\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 3x $ and $ B = 5 $. $$ \left(3x+5\right)^3 = \left( 3x \right)^3+3 \cdot \left( 3x \right)^2 \cdot 5 + 3 \cdot 3x \cdot 5^2+5^3 = 27x^3+135x^2+225x+125 $$ |
| ② | Combine like terms: $$ \color{blue}{1} +27x^3+135x^2+225x+ \color{blue}{125} = 27x^3+135x^2+225x+ \color{blue}{126} $$ |
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