Equation systems with initial component repeated

Quadratic simplification

\begin{aligned} y &= x^2 -9x + 20\\ & = (x-4)(x-5) \end{aligned}

Binomial simplification

\begin{aligned} (x+y)^{3}&=(x+y)(x+y)(x+y)\\ &=xxx+xxy+xyx+{ {xyy}}+yxx+{ {yxy}}+{ {yyx}}+yyy\\ &=x^{3}+3x^{2}y+{ {3xy^{2}}}+y^{3} \end{aligned}

Hölder's inequality

\begin{eqnarray*}\mathbb {P} \left(S_{n}-\mathrm {E} \left[S_{n}\right]\geq t\right)&=&\mathbb {P} \left(e^{s(S_{n}-\mathrm {E} \left[S_{n}\right])}\geq e^{st}\right)\\&\leq& e^{-st}\mathrm {E} \left[e^{s(S_{n}-\mathrm {E} \left[S_{n}\right])}\right]\\&=&e^{-st}\prod _{i=1}^{n}\mathrm {E} \left[e^{s(X_{i}-\mathrm {E} \left[X_{i}\right])}\right]\\&\leq& e^{-st}\prod _{i=1}^{n}e^{\frac {s^{2}(b_{i}-a_{i})^{2}}{8}}\\&=&\exp \left(-st+{\tfrac {1}{8}}s^{2}\sum _{i=1}^{n}(b_{i}-a_{i})^{2}\right)\end{eqnarray*}