Question
Answer
$$2(3a+1)(3a-2)+(3a-1)^2=27a^2-12a-3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(3a+1)(3a-2)+(3a-1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(3a+1)(3a-2)+9a^2-6a+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(6a+2)(3a-2)+9a^2-6a+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}18a^2-12a+6a-4+9a^2-6a+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}18a^2-6a-4+9a^2-6a+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}27a^2-12a-3\end{aligned} $$ | |
| ① | Find $ \left(3a-1\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3a } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(3a-1\right)^2 = \color{blue}{\left( 3a \right)^2} -2 \cdot 3a \cdot 1 + \color{red}{1^2} = 9a^2-6a+1\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( 3a+1\right) $ $$ \color{blue}{2} \cdot \left( 3a+1\right) = 6a+2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{6a+2}\right) $ by each term in $ \left( 3a-2\right) $. $$ \left( \color{blue}{6a+2}\right) \cdot \left( 3a-2\right) = 18a^2-12a+6a-4 $$ |
| ④ | Combine like terms: $$ 18a^2 \color{blue}{-12a} + \color{blue}{6a} -4 = 18a^2 \color{blue}{-6a} -4 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{18a^2} \color{red}{-6a} \color{green}{-4} + \color{blue}{9a^2} \color{red}{-6a} + \color{green}{1} = \color{blue}{27a^2} \color{red}{-12a} \color{green}{-3} $$ |
This page was created using
Simplify polynomials calculator