Question
Answer
$$(x+2h)^2-2(x+h)^2+x^2=2h^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2h)^2-2(x+h)^2+x^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2+4hx+4h^2-2(x^2+2hx+h^2)+x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2+4hx+4h^2-(2x^2+4hx+2h^2)+x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^2+4hx+4h^2-2x^2-4hx-2h^2+x^2 \xlongequal{ } \\[1 em] & \xlongequal{ }x^2+ \cancel{4hx}+4h^2-2x^2 -\cancel{4hx}-2h^2+x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2h^2\end{aligned} $$ | |
| ① | Find $ \left(x+2h\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}{ 2h }$. $$ \begin{aligned}\left(x+2h\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 2h + \color{red}{\left( 2h \right)^2} = x^2+4hx+4h^2\end{aligned} $$Find $ \left(x+h\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}{ h }$. $$ \begin{aligned}\left(x+h\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot h + \color{red}{h^2} = x^2+2hx+h^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x^2+2hx+h^2\right) $ $$ \color{blue}{2} \cdot \left( x^2+2hx+h^2\right) = 2x^2+4hx+2h^2 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2x^2+4hx+2h^2 \right) = -2x^2-4hx-2h^2 $$ |
| ④ | Combine like terms: $$ \color{blue}{x^2} + \, \color{red}{ \cancel{4hx}} \,+ \color{orange}{4h^2} \color{blue}{-2x^2} \, \color{red}{ -\cancel{4hx}} \, \color{orange}{-2h^2} + \color{blue}{x^2} = \color{orange}{2h^2} $$ |
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