Degree of the polynomial $$x2+1+x2$$−$$18+2x2+1+x2$$−$$18is$$ $$____$$.

$$x2+1+x2$$−$$18+x2+1$$−$$x2$$−$$18$$ $$=2$$ $$8C0x2+18+8C2x2+16x2$$−$$12+8C4x2+14x2$$−$$14$$ $$+8C6x2+12x2$$−$$16+8C8x2$$−$$18which$$ has degree $$8$$.

Binomial theorem for positive integral Index

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Degree of the polynomial ${[\sqrt{x^{2} + 1} + \sqrt{x^{2} - 1}]}^{8} + {[\frac{2}{\sqrt{x^{2} + 1} + \sqrt{x^{2} - 1}}]}^{8}$ is ____.

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${[\sqrt{x^{2} + 1} + \sqrt{x^{2} - 1}]}^{8} + {[\sqrt{x^{2} + 1} - \sqrt{x^{2} - 1}]}^{8} = 2 [^{8} C_{0} {(\sqrt{x^{2} + 1})}^{8} +^{8} C_{2} {(\sqrt{x^{2} + 1})}^{6} {(\sqrt{x^{2} - 1})}^{2} +^{8} C_{4} {(\sqrt{x^{2} + 1})}^{4} {(\sqrt{x^{2} - 1})}^{4} +^{8} C_{6} {(\sqrt{x^{2} + 1})}^{2} {(\sqrt{x^{2} - 1})}^{6} +^{8} C_{8} {(\sqrt{x^{2} - 1})}^{8}]$
which has degree 8.

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Binomial theorem for positive integral Index

Remember concepts with our Masterclasses.

Degree of the polynomial x2+1+x2−18+2x2+1+x2−18is ____.

x2+1+x2−18+x2+1−x2−18 =2 8C0x2+18+8C2x2+16x2−12+8C4x2+14x2−14 +8C6x2+12x2−16+8C8x2−18which has degree 8.

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Degree of the polynomial ${[\sqrt{x^{2} + 1} + \sqrt{x^{2} - 1}]}^{8} + {[\frac{2}{\sqrt{x^{2} + 1} + \sqrt{x^{2} - 1}}]}^{8}$ is ____.