Evaluate the following using suitable identities: $(99)^{3}$

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

Expand each of the following,using suitable identities: $(x + 2y + 4z)^2$

Factorise: $3x^{2}-x-4$

Write the following cube in expanded form: $\left[x-\frac{2}{3} y\right]^{3}$

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