Q7. In the binomial expansion of (2

Transcript

00:02 Okay, the problem is asking for the fourth term and the coefficient of the term that has x to a negative 4 for the binomial 2 minus 3 over x to the power 8.

00:18 So the first thing that i did is rewrite the binomial as 2 minus 3 to the x to a negative 1.

00:24 As we have an 8th in the denominator, using the properties of powers, we can rewrite it as x to the negative 1 to the power.

00:32 Of 8.

00:33 So i can relate this to the binomial formula for the pascal triangle.

00:41 So a will be 2, b will be negative 3 to the negative 1.

00:48 And those are the terms that i will use later to calculate the terms that the term is asking for.

00:56 To find expansion, you can use the binomial formula, but also you can use the pascal.

01:03 Triangle.

01:05 Making the pascal triangle is not hard because when the power is zero, any number rise to the zero would be equal zero.

01:15 So it would be equal one, sorry, so the coefficient is one.

01:18 For the power one, a binomial rise to power one would be having two terms with coefficients one.

01:25 Then to find the other coefficients is as simple as adding the two items on the top and then find the coefficient of the world.

01:35 And always the first one and the last one will be one.

01:38 So for power two, i'll start with one, and then add this two, the two, and then i end with one.

01:46 For power three, i start with one, add this two.

01:51 So one plus two is three, two plus one is three, and then the last term is one.

01:56 Starting with one, one plus three is four, three is six, and so on, until i get the value for a power eight the power eight the values you can see i don't know it's hard to move this so power eight we have that the coefficients are one a 28 58 56 70s 78 8 and 1 and the powers will be again let me just rewrite this here because you cannot see.

02:48 Okay, a, the power of a would be decreasing from eight, that is the maximum to zero, eight to the zero here, that is one, and b would be increasing from zero, one, two, three, four, five, six, seven, eight.

03:05 And notice that at every time, the addition of the powers of both terms are equal to eight...

Question

Q7. In the binomial expansion of (2 - 3/x)^8 written in terms of descending powers of x, find: a. The 4th term. b. The coefficient of x^-4

Question

Q7. In the binomial expansion of (2 - 3/x)^8 written in terms of descending powers of x, find: a. The 4th term. b. The coefficient of x^-4

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