Binomial expansion help

[IBtank]

find the value of the term independent of x in the binomiial expansion of the expression (x² - 2/x)³

confused here. help appreciated

[LikeA'13OSS]

Since youre doin SL i dont think you studied permutations and combinations. Youre can either use the pascal triangle or use counting principles for the expansion.

Using counting principles it would be : 3C0(x²)³+ 3C1(x²)²(- 2/x)+3C2(x²)(- 2/x)²+3C3(- 2/x)³

Im not quite sure, but i think its correct. Check it using a pascal triangle

[Godsire]

The best way is to use Pascal triangle (without using permutations/combinations).

The expression (a-b)³can be expanded as a³ - 3a²b + 3ab² - b³

So let's expand your expression, looking for term independent of x:

(x²-2/x)³=

-1st term: x⁶ (that's not what we are looking for)

- 2nd term: -3 * (x²)²* 2/X = -3 * x⁴* 2/x = -6 * x³(again, so calculate another term)

- 3rd term: 3 * x² * (2/x)2 = 3x² * 4/x² = (reducing x^2) = 3 * 4= 12

Therefore term independent of X is the 3rd one and its value is 12.

[FRdupuis]

First of all, you should know that the term independant of x means x⁰ which = 1.

Normally would use the formula t_n+1= nCr * a^n-r * b^r But since the exponent in the question is only 3, you could expand and find the value without x

If the question had an exponent like 7, you may want to use the formula.