Question
Answer
$$(x+2y+3v)^2=9v^2+6vx+12vy+x^2+4xy+4y^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2y+3v)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9v^2+6vx+12vy+x^2+4xy+4y^2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+2y+3v}\right) $ by each term in $ \left( x+2y+3v\right) $. $$ \left( \color{blue}{x+2y+3v}\right) \cdot \left( x+2y+3v\right) = x^2+2xy+3vx+2xy+4y^2+6vy+3vx+6vy+9v^2 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{2xy} + \color{red}{3vx} + \color{blue}{2xy} +4y^2+ \color{green}{6vy} + \color{red}{3vx} + \color{green}{6vy} +9v^2 = \\ = 9v^2+ \color{red}{6vx} + \color{green}{12vy} +x^2+ \color{blue}{4xy} +4y^2 $$ |
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