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.

a plus b whole cube formula

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.

a plus b whole cube formula

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].

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