Question

what is the coefficant x^2 y^3 in the expansion of (2x+y)^5
A.2
B.5
C.40
D.80
C.it does not exist

Answer 1

this is a Binomial expansion

Answer 2

yea that is that is what the quiz is on can u help me

Answer 3

sorry i got that wrong
its

(a = b)^n = a^n + nC1 a(n-1) b^1 + nC2 a(n-2) b ^2 + ...

in your case n = 5 a = 2x and b = y

Answer 4

oohh thats a^(n-1) and a^(n-2)

Answer 5

so whats the answer ?

Answer 6

so for example your second term is
5C1 (2x)^(5-1) (y)^1

so coefficient of 2nd term is

5C1* 2^4 = 5 * 16 = 80

Answer 7

ok i got another ?

Answer 8

can you do this one now - you need term which includes x2 y^3

Answer 9

can u help me get the answers iv only go 10 more minutes on this quiz then we can work on them

Answer 10

The bionomial expansion of (2x-y)^3 is
A.x^3-6x^2y+12y^2-8y^3
B.x^3-3x^2y+3xy^2-y^3
C.2^3(X^3-3X^2Y+3XY^2-Y^3)
D.8x^3-12x^2y+6x^2-y^3

Answer 11

if we write the term as 5Cr (2x)^(n-r) y ^r

we have r = 3 because we need x^2
so your coefficient is 5C3 * 2^2 = 10 * 2^2 * 1 = 40

Answer 12

(a + b)^3 = a^3 + 3ab^2 + 3a^2b + b^3

replace a by 2x and b by -y and see which one you get

Answer 13

so what would the answer be