Expand: $(x+3y-5z)^{2}$

If $a+b+c=9$ and $ab+bc+ca=26$,find $a^{2}+b^{2}+c^{2}$.

If $p(x) = x^{4} - 2x^{3} + 3x^{2} - ax + 3a - 7$ is divided by $(x + 1)$,the remainder is $19$. Find the value of $a$. Also,find the remainder when $p(x)$ is divided by $(x + 2)$.

Verify whether $3$ and $5$ are zeros of the polynomial $x^{2}-x-6$ or not.

Evaluate the following using suitable identities: $(105)^{3}$

Factorise the expression: $\frac{4x^2}{9} - \frac{x}{3} + \frac{1}{16}$