# a plus b whole cube formula

Have you learnt the formula for a plus b whole cube? This formula comes in algebra chapter. The formula a plus b whole cube is one of the identities in algebra. Other than this formula we have so many other identities that we will learn later.

First, we will learn the formula for a plus b whole cube. If you learn this formula then by using this you can write “a minus b whole cube formula” also. What you have to do is just replacing plus sign with minus sign and then simplifying will give you a minus b whole cube formula.

## Below given is the formula of  a plus b whole cube:

a plus b whole cube is written as (a + b) 3.

(a + b) 3 = a3 + b 3 + 3a 2 b + 3 a b 2

or

(a + b) 3 = a3 + b 3 + 3 ab (a + b) (taking 3ab as common)

The above both formulas are correct. According to the problem we need to use the appropriate formula.

### Derivation of a plus b whole cube formula:

Do you know how we got the (a + b) 3 value? Yes, now we will see the derivation of the formula.

We know that (a + b) 3        = (a + b) x (a + b) 2

= (a+b) x (a2+2ab+b2)

= a (a2 + 2 a b + b2) + b (a2 + 2 a b + b2)

= a3 + 2 a2 b + a b2 + a2 b + 2 a b2 + b3

= a3 + b3 + 3 a2 b + 3 a b2

= a3 + b3 + 3 a b (a + b)

#### Important observations in a plus b whole cube formula:

Number of terms is 4 which is one more than power of a plus b whole cube.

Each term degree is 3 which is equal to the power of (a + b) 3.

Example:

If a + b = 20 and ab = 5 then find a3 + b3

Solution:

We know that (a + b) 3 = a3 + b 3 + 3 a b (a + b)

(20)3 = a3 + b 3 + 3 x 5 x 20

8000   = a3 + b 3 + 300

a3 + b 3 = 8000 – 300

= 7700

Hope you have learnt formula and derivation of a plus b whole cube [(a + b) 3].