Question
Answer
$$a(a-b)+b(a-b)=a^2-b^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}a(a-b)+b(a-b)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}a^2-ab+ab-b^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}a^2-b^2\end{aligned} $$ | |
| 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 | Combine like terms: $$ a^2 \, \color{blue}{ -\cancel{ab}} \,+ \, \color{blue}{ \cancel{ab}} \,-b^2 = a^2-b^2 $$ |
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