Question

Find the coefficient of x^3 in the expansion of (2x+5)^6.

Answer 1

have you learned binomial theorem?

Answer 2

yes

Answer 3

okay. so binomial theorem at power 6 will be something like

Answer 4

6C6, 6C5, 6C4, 6C3, 6C2, 6C2,6C1

Answer 5

6C0... and so on.

Answer 6

6C6 is x^6, 6C5 is x^5, 6C4 is x^4, 6C3 is x^3. and 6C3 is 20 if you use calculator. we are close but not done quite yet.

Answer 7

so the coefficient in front would be 20 (number infront of x^3)^3* (constant)^3.

Answer 8

sorry, but the C indicates combinatory. Just use calculator if you are not so sure. it will match with the binomial table you learned if you are in highschool.

Answer 9

20(2^3)*(5^3)

Answer 10

20000

Answer 11

about right.