Question

(2a+1)^3 Решшите плиз

Answer 1

$8a^3 + 12a^2 + 6a + 1$

Answer 2

To expand the expression (2a + 1)^3, we can use the binomial expansion formula, which is:

(a + b)^n = Σ (n choose k) * a^(n-k) * b^k

where n is the exponent, (n choose k) is the binomial coefficient (also known as combinations), and the summation is taken over k from 0 to n.

In this case, a = 2a, b = 1, and n = 3. Let's apply the formula:

(2a + 1)^3 = Σ (3 choose k) * (2a)^(3-k) * 1^k

Now, we'll expand for each value of k:

For k = 0: (3 choose 0) * (2a)^(3-0) * 1^0 = 1 * (2a)^3 * 1 = 8a^3

For k = 1: (3 choose 1) * (2a)^(3-1) * 1^1 = 3 * (2a)^2 * 1 = 12a^2

For k = 2: (3 choose 2) * (2a)^(3-2) * 1^2 = 3 * (2a)^1 * 1^2 = 6a

For k = 3: (3 choose 3) * (2a)^(3-3) * 1^3 = 1 * (2a)^0 * 1^3 = 1

Now, we add all the terms together:

(2a + 1)^3 = 8a^3 + 12a^2 + 6a + 1

So, the expanded form of (2a + 1)^3 is 8a^3 + 12a^2 + 6a + 1.