Using the binomial theorem, Find the first three terms in the expansion of (x-(1/x))^5.
My solution:
C(5,0)x5 + C(5,1)(x4)(-1/x) + C(5,2)(x3)(-1/x)2
x5 + (5)(x4)(-1/x) + 10(x3)(-1/x)2
x5 + (-5x4/x) + 10(x3)(1/x2)
x5 + (-5x3) + 10(x)
x5 -5x3 + 10x
The first three terms are x5, -5x3, and 10x, respectably.
Is this right? Thanks a lot.
I agree.
stan loona
Yes, your solution is correct!
To find the first three terms in the expansion of (x-(1/x))^5 using the binomial theorem, you correctly applied the formula:
(x - (1/x))^5 = C(5,0)x^5 + C(5,1)(x^4)(-1/x) + C(5,2)(x^3)(-1/x)^2
Then, you simplified the expression by evaluating the binomial coefficients:
C(5,0) = 1
C(5,1) = 5
C(5,2) = 10
After simplifying further, you obtained:
x^5 + (-5x^4/x) + 10(x^3)(1/x^2)
x^5 - 5x^3 + 10x
Hence, the first three terms in the expansion are x^5, -5x^3, and 10x, respectively. Well done!