Answer
$$4(1+x)^3+9(1+x)^2-24.207=4x^3+21x^2+30x-11$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4(1+x)^3+9(1+x)^2-24.207& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4(1+3x+3x^2+x^3)+9(1+2x+x^2)-24.207 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4+12x+12x^2+4x^3+9+18x+9x^2-24.207 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^3+21x^2+30x+13-24.207 \xlongequal{ } \\[1 em] & \xlongequal{ }4x^3+21x^2+30x+13-24 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4x^3+21x^2+30x-11\end{aligned} $$ | |
| ① | Find $ \left(1+x\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 1 $ and $ B = x $. $$ \left(1+x\right)^3 = 1^3+3 \cdot 1^2 \cdot x + 3 \cdot 1 \cdot x^2+x^3 = 1+3x+3x^2+x^3 $$Find $ \left(1+x\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 1 } $ and $ B = \color{red}{ x }$. $$ \begin{aligned}\left(1+x\right)^2 = \color{blue}{1^2} +2 \cdot 1 \cdot x + \color{red}{x^2} = 1+2x+x^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{4} $ by $ \left( 1+3x+3x^2+x^3\right) $ $$ \color{blue}{4} \cdot \left( 1+3x+3x^2+x^3\right) = 4+12x+12x^2+4x^3 $$Multiply $ \color{blue}{9} $ by $ \left( 1+2x+x^2\right) $ $$ \color{blue}{9} \cdot \left( 1+2x+x^2\right) = 9+18x+9x^2 $$ |
| ③ | Combine like terms: $$ \color{blue}{4} + \color{red}{12x} + \color{green}{12x^2} +4x^3+ \color{blue}{9} + \color{red}{18x} + \color{green}{9x^2} = 4x^3+ \color{green}{21x^2} + \color{red}{30x} + \color{blue}{13} $$ |
| ④ | Combine like terms: $$ 4x^3+21x^2+30x+ \color{blue}{13} \color{blue}{-24} = 4x^3+21x^2+30x \color{blue}{-11} $$ |
This page was created using
Simplify polynomials calculator