Question
Answer
$$(u+3x)^4=u^4+12u^3x+54u^2x^2+108ux^3+81x^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(u+3x)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}u^4+12u^3x+54u^2x^2+108ux^3+81x^4\end{aligned} $$ | |
| ① | $$ (u+3x)^4 = (u+3x)^2 \cdot (u+3x)^2 $$ |
| ② | Find $ \left(u+3x\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ u } $ and $ B = \color{red}{ 3x }$. $$ \begin{aligned}\left(u+3x\right)^2 = \color{blue}{u^2} +2 \cdot u \cdot 3x + \color{red}{\left( 3x \right)^2} = u^2+6ux+9x^2\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{u^2+6ux+9x^2}\right) $ by each term in $ \left( u^2+6ux+9x^2\right) $. $$ \left( \color{blue}{u^2+6ux+9x^2}\right) \cdot \left( u^2+6ux+9x^2\right) = \\ = u^4+6u^3x+9u^2x^2+6u^3x+36u^2x^2+54ux^3+9u^2x^2+54ux^3+81x^4 $$ |
| ④ | Combine like terms: $$ u^4+ \color{blue}{6u^3x} + \color{red}{9u^2x^2} + \color{blue}{6u^3x} + \color{green}{36u^2x^2} + \color{orange}{54ux^3} + \color{green}{9u^2x^2} + \color{orange}{54ux^3} +81x^4 = \\ = u^4+ \color{blue}{12u^3x} + \color{green}{54u^2x^2} + \color{orange}{108ux^3} +81x^4 $$ |
This page was created using
Simplify polynomials calculator