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