Question
Answer
$$62x^2+(x+2)^2-2x(10-3x-45)=69x^2+74x+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}62x^2+(x+2)^2-2x(10-3x-45)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}62x^2+(x+2)^2-2x(-3x-35) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}62x^2+x^2+4x+4-2x(-3x-35) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}63x^2+4x+4-2x(-3x-35) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}63x^2+4x+4-(-6x^2-70x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}63x^2+4x+4+6x^2+70x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}69x^2+74x+4\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{10} -3x \color{blue}{-45} = -3x \color{blue}{-35} $$ |
| ② | Find $ \left(x+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}{ x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(x+2\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 2 + \color{red}{2^2} = x^2+4x+4\end{aligned} $$ |
| ③ | Combine like terms: $$ \color{blue}{62x^2} + \color{blue}{x^2} +4x+4 = \color{blue}{63x^2} +4x+4 $$ |
| ④ | Multiply $ \color{blue}{2x} $ by $ \left( -3x-35\right) $ $$ \color{blue}{2x} \cdot \left( -3x-35\right) = -6x^2-70x $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -6x^2-70x \right) = 6x^2+70x $$ |
| ⑥ | Combine like terms: $$ \color{blue}{63x^2} + \color{red}{4x} +4+ \color{blue}{6x^2} + \color{red}{70x} = \color{blue}{69x^2} + \color{red}{74x} +4 $$ |
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