Question

Expand (2x - 5y)^5

Answer 1

Okay...we need the Binomial theorem now. Listen up!
Here is a triangle, I put 1s down the sides and at the peak:
1
1 1
1 1
1 1

Answer 2

get paper and draw this out?

Answer 3

It might help, you will need to draw 6 rows of the triangle

Answer 4

Okay, now fill in the blanks of the triangle. Each blank is the sum of the two numbers directly above it. So now the triangle looks like this:

Answer 5

http://upload.wikimedia.org/wikipedia/commons/c/ca/Pascal_triangle_small.png

Answer 6

(2x-5y)^5 has 6 terms, so look at the sixth row of the triangle. It looks like 1 5 10 10 5 1

Answer 7

ok

Answer 8

This means that the answer will have the form 1*x^5 + 5*x^4*y + 10*x^3*y^2 + 10*x^2*y^3 + 5*x*y^4 + 1*y^5. Do you think you know what to do from here?

Answer 9

i have no idea to be honest. do i just need to add everything together?

Answer 10

Pretty much, but instead of x...you have 2x. And instead of y...you have -5y. Try plugging in the numbers and multiplying through and let me know what you get.

Answer 11

is this wright? 32x5 + 400x4y + 2000x3y2 + 5000xy2 + 6250xy4 + 3125y5

Answer 12

You are close...check your + - signs

Answer 13

32x5 - 400x4y + 2000x3y2 - 5000x2y3 + 6250xy4 + 3125y5

Answer 14

is it - 400x4y - 2000x3y2

Answer 15

oh its plus, i just got all of it mixed up in my head

Answer 16

Yes, it is easy to make a careless mistake. Just double check your work and you should be fine. A good thing to check is that the power of the x decreases by one in every term and the power of the y increases by one in every term.