Question
Answer
$$9(2-54x)^2+2(4-4x)^2+18\cdot(2-54x)-4\cdot(4-4x)=26276x^2-2964x+88$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}9(2-54x)^2+2(4-4x)^2+18\cdot(2-54x)-4\cdot(4-4x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9(4-216x+2916x^2)+2(16-32x+16x^2)+18\cdot(2-54x)-4\cdot(4-4x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}36-1944x+26244x^2+32-64x+32x^2+36-972x-(16-16x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}26276x^2-2008x+68+36-972x-(16-16x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}26276x^2-2980x+104-(16-16x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}26276x^2-2980x+104-16+16x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}26276x^2-2964x+88\end{aligned} $$ | |
| ① | Find $ \left(2-54x\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2 } $ and $ B = \color{red}{ 54x }$. $$ \begin{aligned}\left(2-54x\right)^2 = \color{blue}{2^2} -2 \cdot 2 \cdot 54x + \color{red}{\left( 54x \right)^2} = 4-216x+2916x^2\end{aligned} $$Find $ \left(4-4x\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 4 } $ and $ B = \color{red}{ 4x }$. $$ \begin{aligned}\left(4-4x\right)^2 = \color{blue}{4^2} -2 \cdot 4 \cdot 4x + \color{red}{\left( 4x \right)^2} = 16-32x+16x^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{9} $ by $ \left( 4-216x+2916x^2\right) $ $$ \color{blue}{9} \cdot \left( 4-216x+2916x^2\right) = 36-1944x+26244x^2 $$Multiply $ \color{blue}{2} $ by $ \left( 16-32x+16x^2\right) $ $$ \color{blue}{2} \cdot \left( 16-32x+16x^2\right) = 32-64x+32x^2 $$Multiply $ \color{blue}{18} $ by $ \left( 2-54x\right) $ $$ \color{blue}{18} \cdot \left( 2-54x\right) = 36-972x $$Multiply $ \color{blue}{4} $ by $ \left( 4-4x\right) $ $$ \color{blue}{4} \cdot \left( 4-4x\right) = 16-16x $$ |
| ③ | Combine like terms: $$ \color{blue}{36} \color{red}{-1944x} + \color{green}{26244x^2} + \color{blue}{32} \color{red}{-64x} + \color{green}{32x^2} = \color{green}{26276x^2} \color{red}{-2008x} + \color{blue}{68} $$ |
| ④ | Combine like terms: $$ 26276x^2 \color{blue}{-2008x} + \color{red}{68} + \color{red}{36} \color{blue}{-972x} = 26276x^2 \color{blue}{-2980x} + \color{red}{104} $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 16-16x \right) = -16+16x $$ |
| ⑥ | Combine like terms: $$ 26276x^2 \color{blue}{-2980x} + \color{red}{104} \color{red}{-16} + \color{blue}{16x} = 26276x^2 \color{blue}{-2964x} + \color{red}{88} $$ |
This page was created using
Complex Expression calculator