Expand
$\left(x-\frac{1}{2}\right)^{2}$
Write the coefficient of $x^{2}$ in each of the following:
$(i)$ $\frac{\pi}{6} x+x^{2}-1$
$(ii)$ $3 x-5$
Factorise $: x^{3}-x^{2}-17 x-15$
If $a, b, c$ are all non-zero and $a+b+c=0,$ prove that $\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=3$
Using suitable identity, evaluate the following:
$101 \times 102$