Question

Expand the expression.

(4x − 1)^4

Answer 1

hint: \(\bf (4x - 1)^4\implies (4x - 1)(4x - 1)(4x - 1)(4x - 1)\)

unless you're meant to use the binomial theorem

Answer 2

Use the Pascal Triangle and find the fifth row. The fifth row would contain the numbers 1, 4, 6, 4, and 1. These would be the coefficients of the expression.
Now figure out the powers of the expression. (You can figure out the pattern of the exponents in the answer.)
The form of the expression would be something like:
(4x-1)^4 = 4x^4 + (4)4x^3(-1) + (6)4x^2(-1)^2 + (4)4x(-1)^3+(-1)^4
As you can see, the exponent of 4x decreases by 1 each time (starting with ^4 decreasing to ^0) and the exponent of -1 increases by 1 each time.
Now just simplify.
(4x-1)^4 = 4x^4 - 16x^3 + 24x^2 - 16x+ 1