Question
Answer
$$(3x+2)^4=81x^4+216x^3+216x^2+96x+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x+2)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}81x^4+216x^3+216x^2+96x+16\end{aligned} $$ | |
| ① | $$ (3x+2)^4 = (3x+2)^2 \cdot (3x+2)^2 $$ |
| ② | 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 }$. $$ \begin{aligned}\left(3x+2\right)^2 = \color{blue}{\left( 3x \right)^2} +2 \cdot 3x \cdot 2 + \color{red}{2^2} = 9x^2+12x+4\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{9x^2+12x+4}\right) $ by each term in $ \left( 9x^2+12x+4\right) $. $$ \left( \color{blue}{9x^2+12x+4}\right) \cdot \left( 9x^2+12x+4\right) = 81x^4+108x^3+36x^2+108x^3+144x^2+48x+36x^2+48x+16 $$ |
| ④ | Combine like terms: $$ 81x^4+ \color{blue}{108x^3} + \color{red}{36x^2} + \color{blue}{108x^3} + \color{green}{144x^2} + \color{orange}{48x} + \color{green}{36x^2} + \color{orange}{48x} +16 = \\ = 81x^4+ \color{blue}{216x^3} + \color{green}{216x^2} + \color{orange}{96x} +16 $$ |
This page was created using
Simplify polynomials calculator