The expansion of x-1-x-22 is-A- x2-1-x2-4-x-4 x-6B- x2-1-x2-4-x-8 x-6C- 4 x2-x2-x2-4-x-4 x-6D- x2-1x2-x2-4-xx-4 x-4

The correct option is A x^2+1/x^2 + 4/x +4x+6Using the identity ( a+b+c)^2= a^2+b^2+c^2+2ab+2bc+2ca, (x+ 1/x +2 )^2= x^2+(1/x)^2+ 2^2 +2(x)1/x+21/x(2)+2(2)x = ...

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Byju's Answer

Standard VIII

Mathematics

Expansion of (a+b+c)^2

The expansion...

Question

The expansion of $(x + \frac{1}{x} + 2)^{2}$ is :

x^{2} + \frac{1}{x^{2}} + \frac{4}{x} + 4 x + 6

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x^{2} + \frac{1}{x^{2}} + \frac{4}{x} + 8 x + 6

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4 x^{2} + \frac{1}{x^{2}} + \frac{4}{x} + 4 x + 6

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x^{2} + \frac{1}{x^{2}} + \frac{4}{x} + 4 x + 4

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Solution

The correct option is A $x^{2} + \frac{1}{x^{2}} + \frac{4}{x} + 4 x + 6$
Using the identity $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$ ,
$(x + \frac{1}{x} + 2)^{2} = x^{2} + (\frac{1}{x})^{2} + 2^{2} + 2 (x) \frac{1}{x} + 2 \frac{1}{x} (2) + 2 (2) x$
$= x^{2} + \frac{1}{x^{2}} + \frac{4}{x} + 4 x + 6$ .

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for

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The expansion of (x+1x +2)2 is :

The correct option is A x2+1x2 +4x +4x+6Using the identity ( a+b+c)2=a2+b2+c2+2ab+2bc+2ca, (x+1x +2)2=x2+(1x)2+22+2(x)1x+21x(2)+2(2)x =x2+1x2 +4x +4x+6.

The expansion of $(x + \frac{1}{x} + 2)^{2}$ is :