Expanding both sides using the Binomial Theorem:
Left side:(6x-1)^6 = 6C0(6x)^6 + 6C1(6x)^5(-1)^1 + 6C2(6x)^4(-1)^2 + 6C3(6x)^3(-1)^3 + 6C4(6x)^2(-1)^4 + 6C5(6x)(-1)^5 + 6C6(-1)^6= 46656x^6 - 46656x^5 + 23328x^4 - 6216x^3 + 936x^2 - 72x + 1
Right side:(4x-2)^6 = 6C0(4x)^6 + 6C1(4x)^5(-2)^1 + 6C2(4x)^4(-2)^2 + 6C3(4x)^3(-2)^3 + 6C4(4x)^2(-2)^4 + 6C5(4x)(-2)^5 + 6C6(-2)^6= 4096x^6 - 24576x^5 + 49152x^4 - 49152x^3 + 24576x^2 - 6144x + 64
Therefore, (6x-1)^6 ≠ (4x-2)^6.
Expanding both sides using the Binomial Theorem:
Left side:
(6x-1)^6 = 6C0(6x)^6 + 6C1(6x)^5(-1)^1 + 6C2(6x)^4(-1)^2 + 6C3(6x)^3(-1)^3 + 6C4(6x)^2(-1)^4 + 6C5(6x)(-1)^5 + 6C6(-1)^6
= 46656x^6 - 46656x^5 + 23328x^4 - 6216x^3 + 936x^2 - 72x + 1
Right side:
(4x-2)^6 = 6C0(4x)^6 + 6C1(4x)^5(-2)^1 + 6C2(4x)^4(-2)^2 + 6C3(4x)^3(-2)^3 + 6C4(4x)^2(-2)^4 + 6C5(4x)(-2)^5 + 6C6(-2)^6
= 4096x^6 - 24576x^5 + 49152x^4 - 49152x^3 + 24576x^2 - 6144x + 64
Therefore, (6x-1)^6 ≠ (4x-2)^6.