Use pascal’s triangle or the binomial theorem to find the coefficient on the m3 term in the expression of (2m-1)^4

Step-by-step explanation:

According to pascal triangle, in order to expand the expression , the power of a will be reducing by 1 while the power of b will be increasing by until we reach the highest power n. after the expansion, then we fix the coefficients according to pascal triangle. The coefficient of the expansion varies depending on the power of the expansion.

For power of 0. the coefficient is 1

For power of 1. the coefficient is 1, 1

For power of 2. the coefficient is 1, 2, 1

For power of 3. the coefficient is 1, 3, 3, 1

For power of 4. the coefficient is 1,4, 6, 4, 1 and so on

Fixing the coefficient since the power is 4, we will use the coefficient 1,4,6,4,1 according to pascals to have;

This gives the required expansion

x = 17

step-by-step explanation:

1st step: isolate x.

24 - 3x = -27

-24         -24

-3x   =   -51

2nd step: divide.

-3x     =   -51

  3             3

  x       =     17

hope this

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0