Answer:
1,296x^4 – 864x^3 + 216x^2 – 24x + 1
Step-by-step explanation:
From binomial theorem we know that:
[tex](a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4[/tex]
[tex]a^4 = 1,296x^4 = (6x)^4[/tex]
a = 6x
[tex]b^4 =1[/tex]
b = -1 or b = 1
We have to satisfy: [tex]4ab^3 = -24x[/tex]. Using b = -1
[tex]4(6x)(-1)^3 = 24x(-1) = -24x[/tex]
We have to satisfy: [tex]4a^3b = -864x^3[/tex]
[tex]4(6x)^3(-1) = (-4)216x^3 = -864x^3[/tex]
We have to satisfy: 6a^2b^2 = 216x^2
[tex]6(6x)^2(-1)^2 = 6(36)x^2 = 216x^2[/tex]
Then, [tex](6x - 1)^4 = 1,296x^4 - 864x^3 + 216x^2 - 24x + 1[/tex]
