Question
Answer
$$5-2(3x+2)^2+(2x-1)(2x+4)\cdot(6-x)=-4x^3+16x-27$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5-2(3x+2)^2+(2x-1)(2x+4)\cdot(6-x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5-2(9x^2+12x+4)+(2x-1)(2x+4)\cdot(6-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5-(18x^2+24x+8)+(4x^2+8x-2x-4)\cdot(6-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5-(18x^2+24x+8)+(4x^2+6x-4)\cdot(6-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}5-(18x^2+24x+8)+24x^2-4x^3+36x-6x^2-24+4x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}5-(18x^2+24x+8)-4x^3+18x^2+40x-24 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}5-18x^2-24x-8-4x^3+18x^2+40x-24 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}-18x^2-24x-3-4x^3+18x^2+40x-24 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}-4x^3+16x-27\end{aligned} $$ | |
| ① | Find $ \left(3x+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(3x+2\right)^2 = \color{blue}{\left( 3x \right)^2} +2 \cdot 3x \cdot 2 + \color{red}{2^2} = 9x^2+12x+4\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( 9x^2+12x+4\right) $ $$ \color{blue}{2} \cdot \left( 9x^2+12x+4\right) = 18x^2+24x+8 $$ Multiply each term of $ \left( \color{blue}{2x-1}\right) $ by each term in $ \left( 2x+4\right) $. $$ \left( \color{blue}{2x-1}\right) \cdot \left( 2x+4\right) = 4x^2+8x-2x-4 $$ |
| ③ | Combine like terms: $$ 4x^2+ \color{blue}{8x} \color{blue}{-2x} -4 = 4x^2+ \color{blue}{6x} -4 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{4x^2+6x-4}\right) $ by each term in $ \left( 6-x\right) $. $$ \left( \color{blue}{4x^2+6x-4}\right) \cdot \left( 6-x\right) = 24x^2-4x^3+36x-6x^2-24+4x $$ |
| ⑤ | Combine like terms: $$ \color{blue}{24x^2} -4x^3+ \color{red}{36x} \color{blue}{-6x^2} -24+ \color{red}{4x} = -4x^3+ \color{blue}{18x^2} + \color{red}{40x} -24 $$ |
| ⑥ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 18x^2+24x+8 \right) = -18x^2-24x-8 $$ |
| ⑦ | Combine like terms: $$ \color{blue}{5} -18x^2-24x \color{blue}{-8} = -18x^2-24x \color{blue}{-3} $$ |
| ⑧ | Combine like terms: $$ \, \color{blue}{ -\cancel{18x^2}} \, \color{green}{-24x} \color{orange}{-3} -4x^3+ \, \color{blue}{ \cancel{18x^2}} \,+ \color{green}{40x} \color{orange}{-24} = -4x^3+ \color{green}{16x} \color{orange}{-27} $$ |
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