Expand
$(2 x-y-5)^{2}$
$=(2 x)^{2}+(-y)^{2}+(-5)^{2}+2(2 x)(-y)$$+2(-y)(-5)+2(-5)(2 x)$
$=4 x^{2}+y^{2}+25-4 x y+10 y-20 x$
Without finding the cubes, factorise
$(x-2 y)^{3}+(2 y-3 z)^{3}+(3 z-x)^{3}$
Is $x+1$ is a factor of $4 x^{3}+7 x^{2}-2 x-5$ or not ?
By remainder Theorem find the remainder, when $p(x)$ is divided by $g(x),$ where
$p(x)=x^{3}-6 x^{2}+2 x-4, \quad g(x)=1-\frac{3}{2} x$
Evaluate using suitable identities : $(998)^{3}$
The following expressions are polynomials? Justify your answer:
$\frac{1}{x+1}$
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