Question
Answer
$$(3+x)^3+(5-x)^3=24x^2-48x+152$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3+x)^3+(5-x)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}27+27x+9x^2+x^3+125-75x+15x^2-x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}24x^2-48x+152\end{aligned} $$ | |
| 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 $. $$ \left(3+x\right)^3 = 3^3+3 \cdot 3^2 \cdot x + 3 \cdot 3 \cdot x^2+x^3 = 27+27x+9x^2+x^3 $$Find $ \left(5-x\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 5 $ and $ B = x $. $$ \left(5-x\right)^3 = 5^3-3 \cdot 5^2 \cdot x + 3 \cdot 5 \cdot x^2-x^3 = 125-75x+15x^2-x^3 $$ |
| ② | Combine like terms: $$ \color{blue}{27} + \color{red}{27x} + \color{green}{9x^2} + \, \color{orange}{ \cancel{x^3}} \,+ \color{blue}{125} \color{red}{-75x} + \color{green}{15x^2} \, \color{orange}{ -\cancel{x^3}} \, = \color{green}{24x^2} \color{red}{-48x} + \color{blue}{152} $$ |
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