Answer
$$(x+1)^2(10x-3)=10x^3+17x^2+4x-3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+1)^2(10x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x+1)(10x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}10x^3-3x^2+20x^2-6x+10x-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}10x^3+17x^2+4x-3\end{aligned} $$ | |
| ① | Find $ \left(x+1\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}{ 1 }$. $$ \begin{aligned}\left(x+1\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 1 + \color{red}{1^2} = x^2+2x+1\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2+2x+1}\right) $ by each term in $ \left( 10x-3\right) $. $$ \left( \color{blue}{x^2+2x+1}\right) \cdot \left( 10x-3\right) = 10x^3-3x^2+20x^2-6x+10x-3 $$ |
| ③ | Combine like terms: $$ 10x^3 \color{blue}{-3x^2} + \color{blue}{20x^2} \color{red}{-6x} + \color{red}{10x} -3 = 10x^3+ \color{blue}{17x^2} + \color{red}{4x} -3 $$ |
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