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