$(5 x+3)(5 x-3) = \dots$

By the Remainder Theorem,find the remainder when $p(x)$ is divided by $g(x)$,where $p(x) = x^{3} - 6x^{2} + 2x - 4$ and $g(x) = 1 - \frac{3}{2}x$.

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

Expand $(2 x-3)(2 x+5)$.

Without actual division,prove that $2x^4 - 5x^3 + 2x^2 - x + 2$ is divisible by $x^2 - 3x + 2$.

Factorise the expression: $x^{2} + \frac{y^{2}}{4} + \frac{z^{2}}{16} + xy + \frac{yz}{4} + \frac{zx}{2}$