Answer
$$3(a^2+b^2)+2ad-2bc+7(c^2+d^2)=3a^2+2ad+3b^2-2bc+7c^2+7d^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3(a^2+b^2)+2ad-2bc+7(c^2+d^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3a^2+3b^2+2ad-2bc+7c^2+7d^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3a^2+2ad+3b^2-2bc+7c^2+7d^2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( a^2+b^2\right) $ $$ \color{blue}{3} \cdot \left( a^2+b^2\right) = 3a^2+3b^2 $$Multiply $ \color{blue}{7} $ by $ \left( c^2+d^2\right) $ $$ \color{blue}{7} \cdot \left( c^2+d^2\right) = 7c^2+7d^2 $$ |
| ② | Combine like terms: $$ 3a^2+3b^2+2ad-2bc+7c^2+7d^2 = 3a^2+2ad+3b^2-2bc+7c^2+7d^2 $$ |
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