WILL MARK BRAINLIEST! Which of the following is the expansion of (3c+d^2)^6? USE BINOMIAL THEROEMPLEASE GET THIS RIGHT IM STRUGGLING WITH THIS!
Accepted Solution
A:
Answer:(3c+d^2)6=729c^6+1458c^5d^2+1215c^4d^4+540c^3d^6+135c^2d^8+18cd^10+d^12Step-by-step explanation:The expansion is given by the following formula: (a+b)n=βk=0n(nk)anβkbk,where (nk)=n!(nβk)!k! and n!=1β 2β 3...n. Β We have that a=3c, b=d2, n=6.
Therefore, (3c+d2)6=βk=06(6k)(3c)6βk(d2)kNow, calculate the product for every value of k from 0 to 6.
k=0: (60)(3c)6β0(d2)0=6!(6β0)!0!(3c)6(d2)0=729c6
k=1: (61)(3c)6β1(d2)1=6!(6β1)!1!(3c)5(d2)1=1458c5d2
k=2: (62)(3c)6β2(d2)2=6!(6β2)!2!(3c)4(d2)2=1215c4d4
k=3: (63)(3c)6β3(d2)3=6!(6β3)!3!(3c)3(d2)3=540c3d6
k=4: (64)(3c)6β4(d2)4=6!(6β4)!4!(3c)2(d2)4=135c2d8
k=5: (65)(3c)6β5(d2)5=6!(6β5)!5!(3c)1(d2)5=18cd10
k=6: (66)(3c)6β6(d2)6=6!(6β6)!6!(3c)0(d2)6=d12Finally, (3c+d2)6=βk=06(6k)(3c)6βk(d2)k=(60)(3c)6β0(d2)0+(61)(3c)6β1(d2)1+(62)(3c)6β2(d2)2+(63)(3c)6β3(d2)3+(64)(3c)6β4(d2)4+(65)(3c)6β5(d2)5+(66)(3c)6β6(d2)6=729c6+1458c5d2+1215c4d4+540c3d6+135c2d8+18cd10+d12Answer is above :)