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

Give possible expressions for the length and breadth of a rectangle whose area is given as $(20 x^{2}+22 x+6)$ square units,where $(x > 0)$.

Write the following cube in expanded form:
$(7x - 4y)^{3}$

Check whether $p(x)$ is a multiple of $g(x)$ or not:
$p(x) = 2x^3 - 11x^2 - 4x + 5, \quad g(x) = 2x + 1$

The polynomial $p(x) = x^{4} - 2x^{3} + 3x^{2} - ax + 3a - 7$ when divided by $x + 1$ leaves the remainder $19$. Find the value of $a$. Also,find the remainder when $p(x)$ is divided by $x + 2$.

Factorise:
$1+64 x^{3}$