Use the Binomial Theorem to expand each binomial.
(2x - 1)^6
Using the Binomial Theorem, the expansion of (2x - 1)^6 is:
(6 choose 0)(2x)^6(-1)^0 + (6 choose 1)(2x)^5(-1)^1 + (6 choose 2)(2x)^4(-1)^2 + (6 choose 3)(2x)^3(-1)^3 + (6 choose 4)(2x)^2(-1)^4 + (6 choose 5)(2x)^1(-1)^5 + (6 choose 6)(2x)^0(-1)^6
Simplifying each term:
(1)(64x^6)(1) + (6)(32x^5)(-1) + (15)(16x^4)(1) + (20)(8x^3)(-1) + (15)(4x^2)(1) + (6)(2x)(-1) + (1)(1)(-1)
Simplifying further:
64x^6 - 192x^5 + 240x^4 - 160x^3 + 60x^2 - 12x - 1
Therefore, the expansion of (2x - 1)^6 is 64x^6 - 192x^5 + 240x^4 - 160x^3 + 60x^2 - 12x - 1.