Answer
$$(2-a-5b)^2=a^2+10ab+25b^2-4a-20b+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2-a-5b)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}a^2+10ab+25b^2-4a-20b+4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2-a-5b}\right) $ by each term in $ \left( 2-a-5b\right) $. $$ \left( \color{blue}{2-a-5b}\right) \cdot \left( 2-a-5b\right) = 4-2a-10b-2a+a^2+5ab-10b+5ab+25b^2 $$ |
| ② | Combine like terms: $$ 4 \color{blue}{-2a} \color{red}{-10b} \color{blue}{-2a} +a^2+ \color{green}{5ab} \color{red}{-10b} + \color{green}{5ab} +25b^2 = \\ = a^2+ \color{green}{10ab} +25b^2 \color{blue}{-4a} \color{red}{-20b} +4 $$ |
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