Answer
$${(x+a)^2}^2=a^4+4a^3x+6a^2x^2+4ax^3+x^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}{(x+a)^2}^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2ax+a^2)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}a^4+4a^3x+6a^2x^2+4ax^3+x^4\end{aligned} $$ | |
| ① | Find $ \left(x+a\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ a }$. $$ \begin{aligned}\left(x+a\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot a + \color{red}{a^2} = x^2+2ax+a^2\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2+2ax+a^2}\right) $ by each term in $ \left( x^2+2ax+a^2\right) $. $$ \left( \color{blue}{x^2+2ax+a^2}\right) \cdot \left( x^2+2ax+a^2\right) = \\ = x^4+2ax^3+a^2x^2+2ax^3+4a^2x^2+2a^3x+a^2x^2+2a^3x+a^4 $$ |
| ③ | Combine like terms: $$ x^4+ \color{blue}{2ax^3} + \color{red}{a^2x^2} + \color{blue}{2ax^3} + \color{green}{4a^2x^2} + \color{orange}{2a^3x} + \color{green}{a^2x^2} + \color{orange}{2a^3x} +a^4 = \\ = a^4+ \color{orange}{4a^3x} + \color{green}{6a^2x^2} + \color{blue}{4ax^3} +x^4 $$ |
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Simplify Rational Expressions