Please help me with math?

Question

Can anyone help me understand expanding (x+y)^11 using pascel's Triangle? I am cannot remeber the formula and can't find it in my book.

Answer 1

Just write out pascals triangle up to the 12th (11+1) line:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
1 11 55 165 330 462 462 330 165 55 11 1.
Whew.
So those are the coefficients, so you get
x^11 + 11x^10 y + 55x^9 y^2 + 165x^8 y^3 + ... + 11xy^10 + y^11.

Answer 2

I can't do triangles here. Yahoo! Answers doesn't allow triangles.

The coefficients of the 12 terms are

1
11
11 * 10 / 2
11 * 10 * 9 / 3 * 2
11 * 10 * 9 * 8 / 4 * 3 * 2
11 * 10 * 9 * 8 * 7 / 5 * 4 * 3 * 2
11 * 10 * 9 * 8 * 7 / 5 * 4 * 3 * 2
11 * 10 * 9 * 8 / 4 * 3 * 2
11 * 10 * 9 / 3 * 2
11 * 10 / 2
11
1

Do you know the exponents of the 12 terms?

Answer 3

Pascal's triangle determines the coefficient of an expression such as this one.

Basically the exponent, determines which row creates the answer.

For this problem it would be the 11th row:

1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1

Answer 4

the coefficients are found in the eleventh row of Pascal's triangle

The coefficients are 1,11,55,165,330......55,11,1

so the expansion is:

1x^11+11x^10 y + 55x^9 y^2 + 165 x^8 y^3 +.......+ 55x^2 y^9 + 11x y^10 + 1 y^11

Answer 5

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
what you do is you take the top two numbers and add them together. if it was (x+y)^4 it would be

1(x^4+y^0) + 4(x^3+y^1) + 6(x^2+y^2) + 4(x^1+y^3) + 1(x^0 + y^4)

Answer 6

alright firts you multiply 1 by 11 because x is reallly x^1
then u multiply 1 by 11 because y is really y^1
so the answer is x^11+y^11
but if the equation was like (x^3+y^2)^11 it would be x^33+y^22

Answer 7

(x+y)(x+y)(x+y)(x+y)(x+y)(x+y)(x+y)(x+y)(x+y)(x+y)(x+y)

http://ptri1.tripod.com/