Question

What is the fourth term in the expansion of (x+2)6?

480x

168x4

160x3

120x3

Answer 1

\[(x+2)^6=x^6+12 x^5+60 x^4+160 x^3+240 x^2+192 x+64 \]

Answer 2

@robtobey can you explain?

Answer 3

use the formula \[T _{r+1}=_{r}^{n}C(a)^{n-r}(b)^{r}\] for 4th term put r=3 in the formula where n=max power=6 a is first term (term independent of x ie 2) b is the second term ie x

Answer 4

\[T _{3}+1=\frac{ 6 }{3 }C(a)^{3}(b)^{3}\]

Answer 5

is that right so far?

Answer 6

is the answer 160x3?

Answer 7

no that's wrong it should be \[T _{4}=_{3}^{6}C (2)^{3}(x ^{3})\] where C is combination (6C3)

Answer 8

\[T_{4}=2C(8)(x ^{3})\]

Answer 9

is that closer to how you simplify it?

Answer 10

no its not 6/3 C its 6C3 and is evaluated by typing 6 followed by pressing nCr key on your calculator to type C and then typing 3 it should give 20 as answer

Answer 11

The rest is ok the answer should be 160x^3

Answer 12

ohh okay, I get it. Thank you so much!

Answer 13

np :)