If a + b = 1, then the value of a3 + b3 + 3ab is equal to

If a + b = 1, then the value of a³ + b³ + 3ab is equal to
1). 0
2). 1
3). 2
4). 3

We are given the equation:

$a + b = 1$

We need to find the value of:

$a^3 + b^3 + 3ab$

### Step 1: Use the identity for sum of cubes

We know the identity:

$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$

Using the square identity:

$a^2 + b^2 = (a + b)^2 - 2ab$

Substituting $a + b = 1$:

$a^2 + b^2 = 1^2 - 2ab = 1 - 2ab$

Now, substituting in the sum of cubes identity:

$a^3 + b^3 = (1)(1 - 3ab) = 1 - 3ab$

Thus,

$a^3 + b^3 + 3ab = (1 - 3ab) + 3ab = 1$

So, the correct answer is **2) 1**.

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