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

Factorize: $(a-b+c)^{2}+(b-c+a)^{2}+2(a-b+c)(b+c-a)$

If $x+\frac{1}{x}=3,$ then the value of $x^{6}+\frac{1}{x^{6}}$ is

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:

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

If $(x-2)$ is a factor of the polynomial $x^{3}-2ax^{2}+ax-1$,then find the value of $a$.