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