Question

Expand the binomial using the binomial theorem: (3x-4)^5

Can someone explain how you solve this?

Answer 1

Explanation:

We worry about 2 things:

-terms power

-coefficient for each term

(3x-4)^5, has 2 terms 3x and -4

-Start with the first term to the highest power 5 and second term to the lowest power 0, then the high power goes down and low power increases until the first term has the lowest power 0 and the second term has the highest power 5.

-The coefficients for each term we take it from the Pascal triangle.

For the the power 5 the coefficients are 1, 5, 10, 10, 5, 1

`(3x-4)^(5) = 1*(3x)^(5) *(-4)^(0) +5*(3x)^(4) *(-4)^(1) +10*(3x)^(3) *(-4)^(2)+10*(3x)^(2) *(-4)^(3)+5*(3x)^(1) *(-4)^(4)+1*(3x)^(0) *(-4)^(5)`

Simplify:

`(3x-4)^(5) = 3^(5) x^(5) -20*3^(4) x^(4) +160*3^(3) x^(3)-640*3^(2) x^(2)+1280*3x-1024`

`(3x-4)^(5) = 243 x^(5) -1,620x^(4) +4,320 x^(3)-5,760x^(2)+3,840x-1024`