Browse Questions

# The expression $P(x)$ = $\big(\sqrt {x^5-1}+x\big)^7$ - $\big(\sqrt {x^5-1}-x\big)^7$ is a polynomial of what degree?

$\begin{array}{1 1} 16 \\ 18 \\ 20 \\ 27 \end{array}$

Toolbox:
• $(a+b)^n-(a-b)^n=2[^nC_1a^{n-1}.b+^nC_3a^{n-3}.b^3+..........]$
$\big(\sqrt {x^5-1}+x\big)^7-\big(\sqrt {x^5-1}-x\big)^7=$
$2\big[^7C_1.(x^5-1)^3.x+^7C_3.(x^5-1)^2.x^3+^7C_5.(x^5-1).x^5+^7C_7x^7\big]$
which is a poly nomial of degree $16$.