Answer
$$(w+b-6)^2+(2w+b-4)^2+(3w+b-2)^2=3b^2+12bw+14w^2-24b-40w+56$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(w+b-6)^2+(2w+b-4)^2+(3w+b-2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}b^2+2bw+w^2-12b-12w+36+b^2+4bw+4w^2-8b-16w+16+b^2+6bw+9w^2-4b-12w+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2b^2+6bw+5w^2-20b-28w+52+b^2+6bw+9w^2-4b-12w+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}3b^2+12bw+14w^2-24b-40w+56\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{w+b-6}\right) $ by each term in $ \left( w+b-6\right) $. $$ \left( \color{blue}{w+b-6}\right) \cdot \left( w+b-6\right) = w^2+bw-6w+bw+b^2-6b-6w-6b+36 $$ |
| ② | Combine like terms: $$ w^2+ \color{blue}{bw} \color{red}{-6w} + \color{blue}{bw} +b^2 \color{green}{-6b} \color{red}{-6w} \color{green}{-6b} +36 = b^2+ \color{blue}{2bw} +w^2 \color{green}{-12b} \color{red}{-12w} +36 $$Multiply each term of $ \left( \color{blue}{2w+b-4}\right) $ by each term in $ \left( 2w+b-4\right) $. $$ \left( \color{blue}{2w+b-4}\right) \cdot \left( 2w+b-4\right) = 4w^2+2bw-8w+2bw+b^2-4b-8w-4b+16 $$ |
| ③ | Combine like terms: $$ 4w^2+ \color{blue}{2bw} \color{red}{-8w} + \color{blue}{2bw} +b^2 \color{green}{-4b} \color{red}{-8w} \color{green}{-4b} +16 = b^2+ \color{blue}{4bw} +4w^2 \color{green}{-8b} \color{red}{-16w} +16 $$Multiply each term of $ \left( \color{blue}{3w+b-2}\right) $ by each term in $ \left( 3w+b-2\right) $. $$ \left( \color{blue}{3w+b-2}\right) \cdot \left( 3w+b-2\right) = 9w^2+3bw-6w+3bw+b^2-2b-6w-2b+4 $$ |
| ④ | Combine like terms: $$ 9w^2+ \color{blue}{3bw} \color{red}{-6w} + \color{blue}{3bw} +b^2 \color{green}{-2b} \color{red}{-6w} \color{green}{-2b} +4 = b^2+ \color{blue}{6bw} +9w^2 \color{green}{-4b} \color{red}{-12w} +4 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{b^2} + \color{red}{2bw} + \color{green}{w^2} \color{orange}{-12b} \color{blue}{-12w} + \color{red}{36} + \color{blue}{b^2} + \color{red}{4bw} + \color{green}{4w^2} \color{orange}{-8b} \color{blue}{-16w} + \color{red}{16} = \\ = \color{blue}{2b^2} + \color{red}{6bw} + \color{green}{5w^2} \color{orange}{-20b} \color{blue}{-28w} + \color{red}{52} $$ |
| ⑥ | Combine like terms: $$ \color{blue}{2b^2} + \color{red}{6bw} + \color{green}{5w^2} \color{orange}{-20b} \color{blue}{-28w} + \color{red}{52} + \color{blue}{b^2} + \color{red}{6bw} + \color{green}{9w^2} \color{orange}{-4b} \color{blue}{-12w} + \color{red}{4} = \\ = \color{blue}{3b^2} + \color{red}{12bw} + \color{green}{14w^2} \color{orange}{-24b} \color{blue}{-40w} + \color{red}{56} $$ |
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