Tap the blue circles to see an explanation.
| $$ \begin{aligned}(sqrtx-3)^4+3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}q^4r^4s^4t^4x^4-12q^3r^3s^3t^3x^3+54q^2r^2s^2t^2x^2-108qrstx+81+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}q^4r^4s^4t^4x^4-12q^3r^3s^3t^3x^3+54q^2r^2s^2t^2x^2-108qrstx+84\end{aligned} $$ | |
| ① | $$ (qrstx-3)^4 = (qrstx-3)^2 \cdot (qrstx-3)^2 $$ |
| ② | Find $ \left(qrstx-3\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ qrstx } $ and $ B = \color{red}{ 3 }$. $$ \begin{aligned}\left(qrstx-3\right)^2 = \color{blue}{\left( qrstx \right)^2} -2 \cdot qrstx \cdot 3 + \color{red}{3^2} = q^2r^2s^2t^2x^2-6qrstx+9\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{q^2r^2s^2t^2x^2-6qrstx+9}\right) $ by each term in $ \left( q^2r^2s^2t^2x^2-6qrstx+9\right) $. $$ \left( \color{blue}{q^2r^2s^2t^2x^2-6qrstx+9}\right) \cdot \left( q^2r^2s^2t^2x^2-6qrstx+9\right) = \\ = q^4r^4s^4t^4x^4-6q^3r^3s^3t^3x^3+9q^2r^2s^2t^2x^2-6q^3r^3s^3t^3x^3+36q^2r^2s^2t^2x^2-54qrstx+9q^2r^2s^2t^2x^2-54qrstx+81 $$ |
| ④ | Combine like terms: $$ q^4r^4s^4t^4x^4 \color{blue}{-6q^3r^3s^3t^3x^3} + \color{red}{9q^2r^2s^2t^2x^2} \color{blue}{-6q^3r^3s^3t^3x^3} + \color{green}{36q^2r^2s^2t^2x^2} \color{orange}{-54qrstx} + \color{green}{9q^2r^2s^2t^2x^2} \color{orange}{-54qrstx} +81 = \\ = q^4r^4s^4t^4x^4 \color{blue}{-12q^3r^3s^3t^3x^3} + \color{green}{54q^2r^2s^2t^2x^2} \color{orange}{-108qrstx} +81 $$ |
| ⑤ | Combine like terms: $$ q^4r^4s^4t^4x^4-12q^3r^3s^3t^3x^3+54q^2r^2s^2t^2x^2-108qrstx+ \color{blue}{81} + \color{blue}{3} = \\ = q^4r^4s^4t^4x^4-12q^3r^3s^3t^3x^3+54q^2r^2s^2t^2x^2-108qrstx+ \color{blue}{84} $$ |