Question
Answer
$$2(-18a+3)^3+6(-18a+3)(-36a)^2-6(-18a+3)^2-6(-36a)^2=-151632a^3+19440a^2-324a$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(-18a+3)^3+6(-18a+3)(-36a)^2-6(-18a+3)^2-6(-36a)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(27-486a+2916a^2-5832a^3)+6(-18a+3)\cdot1296a^2-6(324a^2-108a+9)-6\cdot1296a^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}54-972a+5832a^2-11664a^3+(-108a+18)\cdot1296a^2-(1944a^2-648a+54)-7776a^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}54-972a+5832a^2-11664a^3-139968a^3+23328a^2-(1944a^2-648a+54)-7776a^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-151632a^3+29160a^2-972a+54-(1944a^2-648a+54)-7776a^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-151632a^3+29160a^2-972a+54-1944a^2+648a-54-7776a^2 \xlongequal{ } \\[1 em] & \xlongequal{ }-151632a^3+29160a^2-972a+ \cancel{54}-1944a^2+648a -\cancel{54}-7776a^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-151632a^3+19440a^2-324a\end{aligned} $$ | |
| ① | Find $ \left(-18a+3\right)^3 $ in two steps. S1: Swap two terms inside bracket S2: apply formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 3 $ and $ B = 18a $. $$ \left(-18a+3\right)^3 \xlongequal{ S1 } \left(3-18a\right)^3 = 3^3-3 \cdot 3^2 \cdot 18a + 3 \cdot 3 \cdot \left( 18a \right)^2-\left( 18a \right)^3 = 27-486a+2916a^2-5832a^3 $$$$ \left( -36a \right)^2 = (-36)^2a^2 = 1296a^2 $$Find $ \left(-18a+3\right)^2 $ in two steps. S1: Change all signs inside bracket. S2: Apply formula $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 18a } $ and $ B = \color{red}{ 3 }$. $$ \begin{aligned}\left(-18a+3\right)^2& \xlongequal{ S1 } \left(18a-3\right)^2 \xlongequal{ S2 } \color{blue}{\left( 18a \right)^2} -2 \cdot 18a \cdot 3 + \color{red}{3^2} = \\[1 em] & = 324a^2-108a+9\end{aligned} $$$$ \left( -36a \right)^2 = (-36)^2a^2 = 1296a^2 $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( 27-486a+2916a^2-5832a^3\right) $ $$ \color{blue}{2} \cdot \left( 27-486a+2916a^2-5832a^3\right) = 54-972a+5832a^2-11664a^3 $$Multiply $ \color{blue}{6} $ by $ \left( -18a+3\right) $ $$ \color{blue}{6} \cdot \left( -18a+3\right) = -108a+18 $$Multiply $ \color{blue}{6} $ by $ \left( 324a^2-108a+9\right) $ $$ \color{blue}{6} \cdot \left( 324a^2-108a+9\right) = 1944a^2-648a+54 $$ |
| ③ | $$ \left( \color{blue}{-108a+18}\right) \cdot 1296a^2 = -139968a^3+23328a^2 $$ |
| ④ | Combine like terms: $$ 54-972a+ \color{blue}{5832a^2} \color{red}{-11664a^3} \color{red}{-139968a^3} + \color{blue}{23328a^2} = \color{red}{-151632a^3} + \color{blue}{29160a^2} -972a+54 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 1944a^2-648a+54 \right) = -1944a^2+648a-54 $$ |
| ⑥ | Combine like terms: $$ -151632a^3+ \color{blue}{29160a^2} \color{red}{-972a} + \, \color{green}{ \cancel{54}} \, \color{blue}{-1944a^2} + \color{red}{648a} \, \color{green}{ -\cancel{54}} \, \color{blue}{-7776a^2} = -151632a^3+ \color{blue}{19440a^2} \color{red}{-324a} $$ |
This page was created using
Simplify polynomials calculator