Factorise the following:
$\left(2 x+\frac{1}{3}\right)^{2}-\left(x-\frac{1}{2}\right)^{2}$
$\left(2 x+\frac{1}{3}\right)^{2}-\left(x-\frac{1}{2}\right)^{2}$
Using identity $a^{2}-b^{2}=(a+b)(a-b)$
$=\left[\left(2 x+\frac{1}{3}\right)+\left(x-\frac{1}{2}\right)\right]\left[\left(2 x+\frac{1}{3}\right)-\left(x-\frac{1}{2}\right)\right]$
$=\left(2 x+\frac{1}{3}+x-\frac{1}{2}\right)\left(2 x+\frac{1}{3}-x+\frac{1}{2}\right)=\left(3 x-\frac{1}{6}\right)\left(x+\frac{5}{6}\right)$
Factorise the following quadratic polynomials by splitting the middle term
$x^{2}+10 x+16$
Give possible expressions for the length and breadth of the rectangle whose area is given by $4 a^{2}+4 a-3$
Factorise :
$2 x^{3}-3 x^{2}-17 x+30$
For what value of $m$ is $x^{3}-2 m x^{2}+16$ divisible by $x+2 ?$
Write the coefficient of $x^{2}$ in the following polynomials
$\sqrt{3} x^{2}+11$