Without actually calculating the cubes, find the value of each of the following

$(14)^{3}+(27)^{3}-(41)^{3}$

Expand the following:

$\left(4-\frac{1}{3 x}\right)^{3}$

For the polynomial $p(x)=x^{2}-7 x+12$ $p(2)=\ldots \ldots . .$

Factorise the following quadratic polynomials by splitting the middle term

$6 x^{2}+19 x+10$

State whether each of the following statements is true or false

In polynomial $5 x^{3}-3 x^{2}+11 x-14,$ the coefficient of $x^{3}$ is $3.$

Factorise $x^{2}-7 x+12$ by using the factor theorem.