Question
Answer
$$(x+2)^3-2(x+3)-3x^2=x^3+3x^2+10x+2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2)^3-2(x+3)-3x^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^3+6x^2+12x+8-2(x+3)-3x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3+6x^2+12x+8-(2x+6)-3x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+6x^2+12x+8-2x-6-3x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+3x^2+10x+2\end{aligned} $$ | |
| ① | Find $ \left(x+2\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = x $ and $ B = 2 $. $$ \left(x+2\right)^3 = x^3+3 \cdot x^2 \cdot 2 + 3 \cdot x \cdot 2^2+2^3 = x^3+6x^2+12x+8 $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x+3\right) $ $$ \color{blue}{2} \cdot \left( x+3\right) = 2x+6 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2x+6 \right) = -2x-6 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{6x^2} + \color{red}{12x} + \color{green}{8} \color{red}{-2x} \color{green}{-6} \color{blue}{-3x^2} = x^3+ \color{blue}{3x^2} + \color{red}{10x} + \color{green}{2} $$ |
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