drinkinwater
drinkinwater drinkinwater
  • 25-05-2019
  • Mathematics
contestada

coefficient of x^2 in expansion of the binomial theorem (2x-1)^4 show your work

Respuesta :

Luv2Teach
Luv2Teach Luv2Teach
  • 30-05-2019

Answer:

24

Step-by-step explanation:

If you use Pascal's triangle, which I did, you will look at the 5th row of the triangle which contains the numbers 1, 4, 6, 4, 1

If we expand using a = 2x and b = -1, then the expansion looks like this:

[tex]1(2x)^4(-1)^0+4(2x)^3(-1)^1+6(2x)^2(-1)^2+4(2x)^1(-1)^3+1(2x)^0(-1)^4[/tex]

If you simplify all that down by multiplying, you'll get

[tex]16x^4-32x^3+24x^2-8x+1[/tex]

If you don't know how to use Pascal's triangle, you need to learn.  It's so very cool!

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