Question
Answer
$$(x-3y-5z)^2=x^2-6xy-10xz+9y^2+30yz+25z^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-3y-5z)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2-6xy-10xz+9y^2+30yz+25z^2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-3y-5z}\right) $ by each term in $ \left( x-3y-5z\right) $. $$ \left( \color{blue}{x-3y-5z}\right) \cdot \left( x-3y-5z\right) = x^2-3xy-5xz-3xy+9y^2+15yz-5xz+15yz+25z^2 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-3xy} \color{red}{-5xz} \color{blue}{-3xy} +9y^2+ \color{green}{15yz} \color{red}{-5xz} + \color{green}{15yz} +25z^2 = \\ = x^2 \color{blue}{-6xy} \color{red}{-10xz} +9y^2+ \color{green}{30yz} +25z^2 $$ |
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