Question

(2x+3y)³ ----------------

Answer 1

Ответ: 8х³+36х²у+54ху²+27у³

Объяснение:

(2x+3y)³=8х³+36х²у+54ху²+27у³

по формуле (а+с)³=а³+3а²с+3ас²+с³

Answer 2

It seems like you want to simplify the expression (2x + 3y)³. To do this, we can use the binomial theorem, which states that:

(x + y)ⁿ = Σ [n choose k] * x^(n-k) * y^k, where Σ is the summation symbol, [n choose k] is the binomial coefficient, and k ranges from 0 to n.

In your case, n = 3, x = 2x, and y = 3y. So, let's apply the binomial theorem:

(2x + 3y)³ = Σ [3 choose k] * (2x)^(3-k) * (3y)^k

Now, we'll expand each term for k = 0, 1, 2, and 3:

For k = 0: [3 choose 0] * (2x)³ * (3y)⁰ = 1 * 8x³ * 1 = 8x³

For k = 1: [3 choose 1] * (2x)² * (3y)¹ = 3 * 4x² * 3y = 36x²y

For k = 2: [3 choose 2] * (2x)¹ * (3y)² = 3 * 2x * 9y² = 54xy²

For k = 3: [3 choose 3] * (2x)⁰ * (3y)³ = 1 * 1 * 27y³ = 27y³

Now, let's sum up all these terms:

(2x + 3y)³ = 8x³ + 36x²y + 54xy² + 27y³

So, the simplified expression for (2x + 3y)³ is:

8x³ + 36x²y + 54xy² + 27y³