Expand the following:
$(-x+2 y-3 z)^{2}$
$(-x+2 y-3 z)^{2}=\{(-x)+2 y+(-3 z)\}^{2}$
$=(-x)^{2}+(2 y)^{2}+(-3 z)^{2}+2(-x)(2 y)+2(2 y)(-3 z)+2(-3 y z)(-x)$
If $a, b, c$ are all non-zero and $a+b+c=0,$ prove that $\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=3$
Factorise
$\frac{x^{2}}{4}+\frac{3 x y}{5}+\frac{9 y^{2}}{25}$
The following expressions are polynomials? Justify your answer:
$\frac{1}{7} a^{3}-\frac{2}{\sqrt{3}} a^{2}+4 a-7$
Factorise the following:
$25 x^{2}+16 y^{2}+4 z^{2}-40 x y+16 y z-20 x z$
$8 x^{3}-26 x^{2}+13 x+5$
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