What is (x+y)^4?

Question

I would like to ask, what is (x+y)^4?

Answer 1

There are two ways to approach this problem. One is by just "FOIL-ing" out the answer: 

(x + y)(x + y)(x + y)(x + y) taking the product of the first two, then multiplying by the third and taking that answer and multiplying by the forth. 

 

However, I suspect that you are studying the binomial expansion theorem, right? 

Pascal's triangle can help us here. We have a fourth degree polynomial with coefficients of one on each of the variables. We need to go to the 5th row of the triangle to choose the leading coefficients and then remember that the exponents are going to increase, in order, on x and decrease on y 

http://en.wikipedia.org/wiki/Pascal's_triangle

 

the coefficients are 1, 4, 6, 4, 1

 

(1)x⁴ + (4)x³y + (6)x²y² + (4)xy³ + (1)y⁴

 

 

Answer 2

Use the binomial expansion. Look it up and see how it works.

(x+y)⁴=x⁴+4x³y+6x²y²+4xy³+y⁴

you start with x⁴ and the variable x decreases in degree while the variable y increases in degree

How do you get the coefficients ?

(4*1)/1=4

(4*3)/2=6

(6*2)/3=4

(1*4)/4=1 where /1, /2, /3, /4 are the 1st, 2nd, 3rd, and 4th terms