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