Expanding $(2x-y+3z{)}^2$, we get, $4x^2+y^2+9z^2-4xy+kxz-6yz$. Find $k$.

Expanding ${\left(5a+b-3c\right)}^2$, we get, $25a^2+b^2+9c^2+10ab-30ac-kbc$. Find $k$.

Expanding ${\left(-a+3b+7c\right)}^2$, we get, $a^2+9b^2+k{c}^2-6ab-14ac+42bc$. Find $k$.

Factorise $4m^2+4n^2+9r^2+8mn-12nr-12mr$.

Factorise $p^2+9q^2+4z^2-6pq+12qz-4pz$.

Factorise $9m^2+25n^2+4p^2+30nm-20np-12mp$.

Factorising $25x^4+y^2+z^2+10x^{2}y+2yz+10z{x}^2$, we get, $(5x^2+y+z{)}^k$. Find $k$.

Find the value of $x^3+\frac{1}{x^3}$ if $x+\frac{1}{x}=6$.

Find the value of $x^3+\frac{1}{x^3}$ if $x+\frac{1}{x}=5$