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