Question
Answer
$$(-3a+b-3)^2+(-a+b-4)^2+(a+b-4)^2+(3a+b-5)^2=20a^2+4b^2-12a-32b+66$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-3a+b-3)^2+(-a+b-4)^2+(a+b-4)^2+(3a+b-5)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}9a^2-6ab+b^2+18a-6b+9+a^2-2ab+b^2+8a-8b+16+a^2+2ab+b^2-8a-8b+16+9a^2+6ab+b^2-30a-10b+25 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}10a^2-8ab+2b^2+26a-14b+25+a^2+2ab+b^2-8a-8b+16+9a^2+6ab+b^2-30a-10b+25 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}11a^2-6ab+3b^2+18a-22b+41+9a^2+6ab+b^2-30a-10b+25 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}20a^2+4b^2-12a-32b+66\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{-3a+b-3}\right) $ by each term in $ \left( -3a+b-3\right) $. $$ \left( \color{blue}{-3a+b-3}\right) \cdot \left( -3a+b-3\right) = 9a^2-3ab+9a-3ab+b^2-3b+9a-3b+9 $$ |
| ② | Combine like terms: $$ 9a^2 \color{blue}{-3ab} + \color{red}{9a} \color{blue}{-3ab} +b^2 \color{green}{-3b} + \color{red}{9a} \color{green}{-3b} +9 = 9a^2 \color{blue}{-6ab} +b^2+ \color{red}{18a} \color{green}{-6b} +9 $$Multiply each term of $ \left( \color{blue}{-a+b-4}\right) $ by each term in $ \left( -a+b-4\right) $. $$ \left( \color{blue}{-a+b-4}\right) \cdot \left( -a+b-4\right) = a^2-ab+4a-ab+b^2-4b+4a-4b+16 $$ |
| ③ | Combine like terms: $$ a^2 \color{blue}{-ab} + \color{red}{4a} \color{blue}{-ab} +b^2 \color{green}{-4b} + \color{red}{4a} \color{green}{-4b} +16 = a^2 \color{blue}{-2ab} +b^2+ \color{red}{8a} \color{green}{-8b} +16 $$Multiply each term of $ \left( \color{blue}{a+b-4}\right) $ by each term in $ \left( a+b-4\right) $. $$ \left( \color{blue}{a+b-4}\right) \cdot \left( a+b-4\right) = a^2+ab-4a+ab+b^2-4b-4a-4b+16 $$ |
| ④ | Combine like terms: $$ a^2+ \color{blue}{ab} \color{red}{-4a} + \color{blue}{ab} +b^2 \color{green}{-4b} \color{red}{-4a} \color{green}{-4b} +16 = a^2+ \color{blue}{2ab} +b^2 \color{red}{-8a} \color{green}{-8b} +16 $$Multiply each term of $ \left( \color{blue}{3a+b-5}\right) $ by each term in $ \left( 3a+b-5\right) $. $$ \left( \color{blue}{3a+b-5}\right) \cdot \left( 3a+b-5\right) = 9a^2+3ab-15a+3ab+b^2-5b-15a-5b+25 $$ |
| ⑤ | Combine like terms: $$ 9a^2+ \color{blue}{3ab} \color{red}{-15a} + \color{blue}{3ab} +b^2 \color{green}{-5b} \color{red}{-15a} \color{green}{-5b} +25 = \\ = 9a^2+ \color{blue}{6ab} +b^2 \color{red}{-30a} \color{green}{-10b} +25 $$ |
| ⑥ | Combine like terms: $$ \color{blue}{9a^2} \color{red}{-6ab} + \color{green}{b^2} + \color{orange}{18a} \color{blue}{-6b} + \color{red}{9} + \color{blue}{a^2} \color{red}{-2ab} + \color{green}{b^2} + \color{orange}{8a} \color{blue}{-8b} + \color{red}{16} = \\ = \color{blue}{10a^2} \color{red}{-8ab} + \color{green}{2b^2} + \color{orange}{26a} \color{blue}{-14b} + \color{red}{25} $$ |
| ⑦ | Combine like terms: $$ \color{blue}{10a^2} \color{red}{-8ab} + \color{green}{2b^2} + \color{orange}{26a} \color{blue}{-14b} + \color{red}{25} + \color{blue}{a^2} + \color{red}{2ab} + \color{green}{b^2} \color{orange}{-8a} \color{blue}{-8b} + \color{red}{16} = \\ = \color{blue}{11a^2} \color{red}{-6ab} + \color{green}{3b^2} + \color{orange}{18a} \color{blue}{-22b} + \color{red}{41} $$ |
| ⑧ | Combine like terms: $$ \color{blue}{11a^2} \, \color{red}{ -\cancel{6ab}} \,+ \color{orange}{3b^2} + \color{blue}{18a} \color{red}{-22b} + \color{green}{41} + \color{blue}{9a^2} + \, \color{red}{ \cancel{6ab}} \,+ \color{orange}{b^2} \color{blue}{-30a} \color{red}{-10b} + \color{green}{25} = \\ = \color{blue}{20a^2} + \color{orange}{4b^2} \color{blue}{-12a} \color{red}{-32b} + \color{green}{66} $$ |
This page was created using
Simplify polynomials calculator