Evaluate the following using suitable identities: $(998)^{3}$

Factorise the following using appropriate identities : $4 y^{2}-4 y+1$

Find the remainder when $x^{3}+3x^{2}+3x+1$ is divided by $x-\frac{1}{2}$.

Write the following cube in the expanded form: $(3a + 4b)^3$

Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases: $p(x) = x^3 - 4x^2 + x + 6$,$g(x) = x - 3$.

Determine whether $(x + 1)$ is a factor of the polynomial $p(x) = x^{4} + x^{3} + x^{2} + x + 1$.