Question
Answer
$${(2(x+y))^2}^2=16x^4+64x^3y+96x^2y^2+64xy^3+16y^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}{(2(x+y))^2}^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}{(2x+2y)^2}^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(4x^2+8xy+4y^2)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}16x^4+64x^3y+96x^2y^2+64xy^3+16y^4\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( x+y\right) $ $$ \color{blue}{2} \cdot \left( x+y\right) = 2x+2y $$ |
| ② | Find $ \left(2x+2y\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}{ 2y }$. $$ \begin{aligned}\left(2x+2y\right)^2 = \color{blue}{\left( 2x \right)^2} +2 \cdot 2x \cdot 2y + \color{red}{\left( 2y \right)^2} = 4x^2+8xy+4y^2\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{4x^2+8xy+4y^2}\right) $ by each term in $ \left( 4x^2+8xy+4y^2\right) $. $$ \left( \color{blue}{4x^2+8xy+4y^2}\right) \cdot \left( 4x^2+8xy+4y^2\right) = \\ = 16x^4+32x^3y+16x^2y^2+32x^3y+64x^2y^2+32xy^3+16x^2y^2+32xy^3+16y^4 $$ |
| ④ | Combine like terms: $$ 16x^4+ \color{blue}{32x^3y} + \color{red}{16x^2y^2} + \color{blue}{32x^3y} + \color{green}{64x^2y^2} + \color{orange}{32xy^3} + \color{green}{16x^2y^2} + \color{orange}{32xy^3} +16y^4 = \\ = 16x^4+ \color{blue}{64x^3y} + \color{green}{96x^2y^2} + \color{orange}{64xy^3} +16y^4 $$ |
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