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