Resolve into factors: $4 x^{2}+12 x y+9 y^{2}-8 x-12 y$

If $\frac{x}{y} + \frac{y}{x} = 6,$ then find the value of $\frac{x^{3}}{y^{3}} + \frac{y^{3}}{x^{3}}.$

What is the digit in the unit's place in the number $\frac{151}{100}$?

Factorize: $a^{2}+\frac{1}{a^{2}}+3-2 a-\frac{2}{a}$

Find the values of $m$ and $n$ in the polynomial $2x^{3} + mx^{2} + nx - 14$,such that $(x-1)$ and $(x+2)$ are its factors.

Let $f(x) = a_{0}x^{n} + a_{1}x^{n-1} + a_{2}x^{n-2} + \ldots + a_{n-1}x + a_{n}$,where $a_{0}, a_{1}, a_{2}, \ldots, a_{n}$ are constants. If $f(x)$ is divided by $ax - b$,then the remainder is: