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in Binomial Theorem by (42.5k points)
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Find the term independent of x in the expansion of (91 + x + 2x3) \(\Big(\frac{3}{2}x^2 - \frac{1}{3x}\Big)^9\)

1 Answer

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Best answer

To Find : term independent of x, i.e. coefficient of x0 

Formula: tr+1 = (rn) an-rbr

We have a formula, 

tr+1 = (rn) an-rbr

Therefore, the expansion of \(\Big(x-\frac{2}{x}\Big)^{10}\) is given by,

Multiplying the second bracket by 91, x and 2x3

In the first bracket, there will be a 6th term of x0 having coefficient 91 (-2)5(510)

While in the second and third bracket, the constant term is absent. 

Therefore, the coefficient of term independent of x, i.e. constant term in the above expansion

= 91 (-2)5(510)

= 91(-2)5 \(\frac{10\times9\times8\times7\times6}{5\times4\times3\times2\times1}\) 

= – 91(2)5 (252) 

Conclusion: coefficient of term independent of x =-91(2)5 (252)

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