Resolve into factors: $(a+b)^{2}-14 c(a+b)+49 c^{2}$.

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

What is the value of $\frac{(a^{2}+b^{2})(a-b)-(a-b)^{3}}{a^{2}b-ab^{2}}$?

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:

Find the value of $k$ if $f(x) = x^{3} - kx^{2} + 11x - 6$ and $(x - 1)$ is a factor of $f(x)$.

Divide the polynomial $4y^{3}-3y^{2}+2y-4$ by $y+2$ and find the quotient and remainder.