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

Resolve into factors: $16(x-y)^{2}-9(x+y)^{2}$

What is the value of $\left(\frac{x^{2}-x-6}{x^{2}+x-12}\right) \div \left(\frac{x^{2}+5x+6}{x^{2}+7x+12}\right)?$

If $\sqrt{x}+\frac{1}{\sqrt{x}}=5,$ what will be the value of $x^{2}+\frac{1}{x^{2}}$?

When a polynomial $f(x)$ is divided by $x-3$ and $x+6,$ the respective remainders are $7$ and $22.$ What is the remainder when $f(x)$ is divided by $(x-3)(x+6)?$

Factorize: $45 a^{3} b + 5 a b^{3} - 30 a^{2} b^{2}$