Question

(X+2y)^2 A.x^2+4xy+y^2

Answer 1

(x+2y)^2=x^2+4xy+4y^2

Answer 2

To simplify the expression (x + 2y)^2, you can expand it using the binomial theorem.

The binomial theorem states that for any real numbers a and b, and a positive integer n, the expansion of (a + b)^n is given by:

(a + b)^n = C(n,0) * a^n * b^0 + C(n,1) * a^(n-1) * b^1 + C(n,2) * a^(n-2) * b^2 + ... + C(n,n-1) * a^1 * b^(n-1) + C(n,n) * a^0 * b^n,

where C(n, k) is the binomial coefficient, also known as "n choose k," given by C(n, k) = n! / (k! * (n - k)!).

In this case, (x + 2y)^2 can be expanded as follows:

(x + 2y)^2 = C(2,0) * x^2 * (2y)^0 + C(2,1) * x^1 * (2y)^1 + C(2,2) * x^0 * (2y)^2 = 1 * x^2 * 1 + 2 * x^1 * 2y + 1 * x^0 * (2y)^2 = x^2 + 4xy + 4y^2.

Therefore, the simplified expression is x^2 + 4xy + 4y^2.

Please note that the expansion and simplification assume that x and y are real numbers.