(x+y)^3 expand
(a + b)^3= a^3 + 3*a^2*b + 3*a*b^2 + b^3
(x+y)^3= x^3 + 3*x^2*y + 3*x*y^2 + y^3
and also look up "binomial expansion" and "Pascal's triangle". I will post links in a second.
and also look up "binomial expansion" and "Pascal's triangle". I will post links in a second.
here;
http://www.regentsprep.org/Regents/math/algtrig/ATP4/bintheorem.htm
http://en.wikipedia.org/wiki/Pascal%27s_triangle
To expand the expression (x + y)^3, you can use the binomial expansion formula or the Pascal's triangle method.
Using the binomial expansion formula, the expanded form of (x + y)^3 can be found by raising each term in the binomial to the corresponding powers and then multiplying them together.
The binomial expansion formula for (x + y)^3 is:
(x + y)^3 = C(3,0) * x^3 * y^0 + C(3,1) * x^2 * y^1 + C(3,2) * x^1 * y^2 + C(3,3) * x^0 * y^3
The values in the parentheses, such as C(3,0), C(3,1), etc., represent the binomial coefficients. These coefficients can be calculated using the formula:
C(n, r) = n! / (r! * (n-r)!)
Let's calculate the expanded form step by step:
C(3,0) = 3! / (0! * (3-0)!) = 1
C(3,1) = 3! / (1! * (3-1)!) = 3
C(3,2) = 3! / (2! * (3-2)!) = 3
C(3,3) = 3! / (3! * (3-3)!) = 1
Now, substitute the values of coefficients and simplify:
(x + y)^3 = 1*x^3*y^0 + 3*x^2*y^1 + 3*x^1*y^2 + 1*x^0*y^3
= x^3 + 3x^2y + 3xy^2 + y^3
Therefore, the expanded form of (x + y)^3 is x^3 + 3x^2y + 3xy^2 + y^3.