If $x+y=12$ and $x y=27,$ find the value of $x^{3}+y^{3}$
$756$
$780$
$126$
$263$
$x^{3}+y^{3}$
$=(x+y)^{3}-3 x y(x+y)$
$=12^{3}-3 \times 27 \times 12$
$=12\left[12^{2}-3 \times 27\right]$
$=12 \times 63=756$
Factorise
$8 x^{3}-26 x^{2}+13 x+5$
Show that :
$2 x-3$ is a factor of $x+2 x^{3}-9 x^{2}+12$
Check whether $p(x)$ is a multiple of $g(x)$ or not :
$p(x)=2 x^{3}-11 x^{2}-4 x+5, \quad g(x)=2 x+1$
Expand
$(5 x-7 y-z)^{2}$
Evaluate the following products without multiplying directly
$93 \times 95$
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