Answer:
Step-by-step explanation:
We worry about 2 things:
-terms power
-coefficient for each term
(3x-4)^5, has 2 terms 3x and -4
-Start with the first term to the highest power 5 and second term to the lowest power 0, then the high power goes down and low power increases until the first term has the lowest power 0 and the second term has the highest power 5.
-The coefficients for each term we take it from the Pascal triangle.
For the the power 5 the coefficients are 1, 5, 10, 10, 5, 1
[tex](3x-4)^{5} = 1*(3x)^{5} *(-4)^{0} +5*(3x)^{4} *(-4)^{1} +10*(3x)^{3} *(-4)^{2}+10*(3x)^{2} *(-4)^{3}+5*(3x)^{1} *(-4)^{4}+1*(3x)^{0} *(-4)^{5}[/tex]
Simplify:
[tex](3x-4)^{5} = 3^{5} x^{5} -20*3^{4} x^{4} +160*3^{3} x^{3}-640*3^{2} x^{2}+1280*3x-1024[/tex]
[tex](3x-4)^{5} = 243 x^{5} -1,620x^{4} +4,320 x^{3}-5,760x^{2}+3,840x-1024[/tex]
