Question
Answer
$$(3x-5y)^4=81x^4-540x^3y+1350x^2y^2-1500xy^3+625y^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x-5y)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}81x^4-540x^3y+1350x^2y^2-1500xy^3+625y^4\end{aligned} $$ | |
| ① | $$ (3x-5y)^4 = (3x-5y)^2 \cdot (3x-5y)^2 $$ |
| ② | Find $ \left(3x-5y\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}{ 5y }$. $$ \begin{aligned}\left(3x-5y\right)^2 = \color{blue}{\left( 3x \right)^2} -2 \cdot 3x \cdot 5y + \color{red}{\left( 5y \right)^2} = 9x^2-30xy+25y^2\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{9x^2-30xy+25y^2}\right) $ by each term in $ \left( 9x^2-30xy+25y^2\right) $. $$ \left( \color{blue}{9x^2-30xy+25y^2}\right) \cdot \left( 9x^2-30xy+25y^2\right) = \\ = 81x^4-270x^3y+225x^2y^2-270x^3y+900x^2y^2-750xy^3+225x^2y^2-750xy^3+625y^4 $$ |
| ④ | Combine like terms: $$ 81x^4 \color{blue}{-270x^3y} + \color{red}{225x^2y^2} \color{blue}{-270x^3y} + \color{green}{900x^2y^2} \color{orange}{-750xy^3} + \color{green}{225x^2y^2} \color{orange}{-750xy^3} +625y^4 = \\ = 81x^4 \color{blue}{-540x^3y} + \color{green}{1350x^2y^2} \color{orange}{-1500xy^3} +625y^4 $$ |
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