What is the expansion of binomial (x+y)4 (4 is the exponent)

(x+y)^4=(x+y)(x+y)(x+y)(x+y)
we can use pascal's triangle
0: 1
1: 1 1
2: 1 2 1
3: 1 3 3 1
4: 1 4 6 4 1
5: 1 5 10 10 5 1
those are the coefients of the terms for (a+b)^n, all the wa to (a+b)^5

you have to know that the first term for (a+b)^n is always going to be 1(a^n)(b^0)
and lasst term is (a^0)(b^n)
and the n in the a^n decreases as the n in b^n increases
the exponent of both add to n

so

we see the 4 row
4: 1 4 6 4 1
the coefients are 1,4,6,4,1

it goes
1x⁴y⁰+4x³y¹+6x²y²+4x¹y³+1x⁰y⁴ or
x⁴+4x³y+6x²y²+4xy³+y⁴

The answer is -pie over 2