$\lim_{x\to2}\left(\frac{\sin\left(3x^2-12\right)}{x-2}\right)$

$\lim_{x\to\infty}\:\frac{7^n}{4^n}$

$3+2\cdot10+\left(1-\left(12+1\right)\right)-8-8\cdot\left(-2\right)$

$y'+y=xy^4$

$100z^2+200yz+100y^2$

$27x^{7\:}-15x^4$

$\left(x+\frac{3}{5}\right)\left(x+\frac{2}{5}\right)$