Answer
$$(2a^2+dab+2b^2)^2=a^2b^2d^2+4a^3bd+4ab^3d+4a^4+8a^2b^2+4b^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2a^2+dab+2b^2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}a^2b^2d^2+4a^3bd+4ab^3d+4a^4+8a^2b^2+4b^4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2a^2+abd+2b^2}\right) $ by each term in $ \left( 2a^2+abd+2b^2\right) $. $$ \left( \color{blue}{2a^2+abd+2b^2}\right) \cdot \left( 2a^2+abd+2b^2\right) = \\ = 4a^4+2a^3bd+4a^2b^2+2a^3bd+a^2b^2d^2+2ab^3d+4a^2b^2+2ab^3d+4b^4 $$ |
| ② | Combine like terms: $$ 4a^4+ \color{blue}{2a^3bd} + \color{red}{4a^2b^2} + \color{blue}{2a^3bd} +a^2b^2d^2+ \color{green}{2ab^3d} + \color{red}{4a^2b^2} + \color{green}{2ab^3d} +4b^4 = \\ = a^2b^2d^2+ \color{blue}{4a^3bd} + \color{green}{4ab^3d} +4a^4+ \color{red}{8a^2b^2} +4b^4 $$ |
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