Question
Answer
$$-\dfrac{(a+b-1)^2}{2}=-\dfrac{a^2+2ab+b^2-2a-2b+1}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-\frac{(a+b-1)^2}{2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{a^2+2ab+b^2-2a-2b+1}{2}\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{a+b-1}\right) $ by each term in $ \left( a+b-1\right) $. $$ \left( \color{blue}{a+b-1}\right) \cdot \left( a+b-1\right) = a^2+ab-a+ab+b^2-b-a-b+1 $$ |
| ② | Combine like terms: $$ a^2+ \color{blue}{ab} \color{red}{-a} + \color{blue}{ab} +b^2 \color{green}{-b} \color{red}{-a} \color{green}{-b} +1 = a^2+ \color{blue}{2ab} +b^2 \color{red}{-2a} \color{green}{-2b} +1 $$ |
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