Use suitable identities to find the products: $(3-2 x)(3+2 x)$

Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases: $p(x) = 2x^3 + x^2 - 2x - 1$,$g(x) = x + 1$.

Find the zero of the polynomial: $p(x) = ax, a \neq 0$.

Factorise: $8 a^{3}+b^{3}+12 a^{2} b+6 a b^{2}$

Factorise: $2x^2 + y^2 + 8z^2 - 2sqrt{2}xy + 4sqrt{2}yz - 8xz$

Without actually calculating the cubes,find the value of each of the following: $(-12)^{3} + (7)^{3} + (5)^{3}$