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} = a^{3} + b ^{3} + 3a^{ 2} b + 3 a b ^{2}**

or

**(a + b) ^{3} = a^{3} + 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 (a^{2}+2ab+b^{2})

= a (a^{2} + 2 a b + b^{2}) + b (a^{2} + 2 a b + b^{2})

= a^{3} + 2 a^{2} b + a b^{2} + a^{2} b + 2 a b^{2} + b^{3 }

= a^{3 }+ b^{3} + 3 a^{2} b + 3 a b^{2 }

= a^{3} + b^{3} + 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 a^{3} + b^{3}

Solution:

We know that (a + b) ^{3} = a^{3} + b ^{3} + 3 a b (a + b)

(20)^{3} = a^{3} + b ^{3} + 3 x 5 x 20

8000 = a^{3} + b ^{3} + 300

a^{3} + b ^{3} = 8000 – 300

= 7700

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

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