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Find the coefficient of x ^ 4 in the expansion of (1 + x-2x ^ 2) (x + 1 / x) ^ 8
(1+x-2x^2)(x+1/x)^8
=(1+x-2x^2)[ x^8+8x^6+28x^4+56x^2+70+56(1/x^2)+28(1/x^4)+8(1/x^6)+1/x^8 ]
coef.of x^4
=1(28)-2(56)
=-84
In the expansion of (x + 1 / 2x) ^ 8, the coefficient of x ^ 2 is?
Using the general term formula of expansion, this kind of problems are solved in this way. After simplifying the formula, let the coefficient of X be 2, then R can be solved, and the coefficient can be calculated!
In the expansion of (1-x ^ 2) (1 + 2x ^ 2) 12, what is the coefficient of x ^ 8?
(1-x^2)(1+2x^2)^12
=(1+2x^2)^12-x^2(1+2x^2)^12
The coefficient with x ^ 8 in the expansion of (1 + 2x ^ 2) ^ 12 is C (4,12) 2 ^ 4
The coefficient of x ^ 8 in the expansion of x ^ 2 (1 + 2x ^ 2) ^ 12 is C (3,12) 2 ^ 3
So in the expansion of (1-x ^ 2) (1 + 2x ^ 2) ^ 12,
The coefficient of x ^ 8 is C (4,12) 2 ^ 4-C (3,12) 2 ^ 3 = 7920-1760 = 6160
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