Answer
$$(y+2x)^4=16x^4+32x^3y+24x^2y^2+8xy^3+y^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(y+2x)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}16x^4+32x^3y+24x^2y^2+8xy^3+y^4\end{aligned} $$ | |
| ① | $$ (y+2x)^4 = (y+2x)^2 \cdot (y+2x)^2 $$ |
| ② | Find $ \left(y+2x\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ y } $ and $ B = \color{red}{ 2x }$. $$ \begin{aligned}\left(y+2x\right)^2 = \color{blue}{y^2} +2 \cdot y \cdot 2x + \color{red}{\left( 2x \right)^2} = y^2+4xy+4x^2\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{y^2+4xy+4x^2}\right) $ by each term in $ \left( y^2+4xy+4x^2\right) $. $$ \left( \color{blue}{y^2+4xy+4x^2}\right) \cdot \left( y^2+4xy+4x^2\right) = \\ = y^4+4xy^3+4x^2y^2+4xy^3+16x^2y^2+16x^3y+4x^2y^2+16x^3y+16x^4 $$ |
| ④ | Combine like terms: $$ y^4+ \color{blue}{4xy^3} + \color{red}{4x^2y^2} + \color{blue}{4xy^3} + \color{green}{16x^2y^2} + \color{orange}{16x^3y} + \color{green}{4x^2y^2} + \color{orange}{16x^3y} +16x^4 = \\ = 16x^4+ \color{orange}{32x^3y} + \color{green}{24x^2y^2} + \color{blue}{8xy^3} +y^4 $$ |
This page was created using
Simplify polynomials calculator