Question
Answer
$$(32x+2)^2-290(x^2-1)(x+23)=-290x^3-5646x^2+418x+6674$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(32x+2)^2-290(x^2-1)(x+23)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}1024x^2+128x+4-290(x^2-1)(x+23) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1024x^2+128x+4-(290x^2-290)(x+23) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}1024x^2+128x+4-(290x^3+6670x^2-290x-6670) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}1024x^2+128x+4-290x^3-6670x^2+290x+6670 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-290x^3-5646x^2+418x+6674\end{aligned} $$ | |
| ① | Find $ \left(32x+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 32x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(32x+2\right)^2 = \color{blue}{\left( 32x \right)^2} +2 \cdot 32x \cdot 2 + \color{red}{2^2} = 1024x^2+128x+4\end{aligned} $$ |
| ② | Multiply $ \color{blue}{290} $ by $ \left( x^2-1\right) $ $$ \color{blue}{290} \cdot \left( x^2-1\right) = 290x^2-290 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{290x^2-290}\right) $ by each term in $ \left( x+23\right) $. $$ \left( \color{blue}{290x^2-290}\right) \cdot \left( x+23\right) = 290x^3+6670x^2-290x-6670 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 290x^3+6670x^2-290x-6670 \right) = -290x^3-6670x^2+290x+6670 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{1024x^2} + \color{red}{128x} + \color{green}{4} -290x^3 \color{blue}{-6670x^2} + \color{red}{290x} + \color{green}{6670} = \\ = -290x^3 \color{blue}{-5646x^2} + \color{red}{418x} + \color{green}{6674} $$ |
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