A minus B Whole Cube Formula

Explanation of A-B Whole Cube Formula

The explanations with examples of the formula (a - b)3 are given below

(a-b)3 Formula Definition

Basics:-. This (a - b)3 formula is one of the algebraic identities which is used to find the cube of a binomial. The (a - b)3 formula is used to find the cube of the difference between the two terms. The (a - b)3 formula is called identity as this formula is valid for every value of 'a' and 'b'. The (a -b)3 formula is used to factorize the trinomials. The explanations with examples of the formula (a - b)3 are given below

Explanation of (a-b)3 Formula

The algebraic identity is used to find the cube of binomials. To find the formula , we will first write

(a - b)3 = (a - b)(a - b)(a - b)

(a - b)3 = (a2 - 2ab + b2)(a - b)

(a - b)3 = a3 - a2b - 2a2b + 2ab2 + ab2 - b3

(a - b)3 = a3- 32b + 3ab2 - b3

(a - b)3 = a3 - 3ab(a-b) - b3

Therefore, (a - b)3 formula is:

(a - b)3 = a3 - 32b + 3ab2 - b3

Examples on (a-b)3 Formula

Example 1:

Expand (3a-2b)3

Solution

Putting 3a = x and 2b = y, we get

(3a-2b)3 = (x−y)3

=x3-y3-3xy(x−y)

= (3a) 3-(2b)3-(3 × 3a ×2b) (3a-2b)

- 27a3-8b3-18ab (3a − 2b)

= 27a3-8b3-54a2b +36ab2.

Example 2: Factorise

27-125a3-135a +225a

Solution We have

27-125a3-135a + 225a3

= 33-(5a)3-45a(3-5a)

=33-(5a)3-(3x3 x 5a) (3-5a)

= (3-5a)3 = (3-5a) (3-5a) (3-5a).

Example 3: Evaluate (999)³ by using (a - b)3 Formula

Solution

(999)3 = (1000 – 1)3

= (1000) 3 – 13 – (3 × 1000 × 1) (1000-1) 3

=1000000000-1-(3000 × 999)

=999999999 – 2997000

=997002999

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A minus B Whole Cube Formula
A minus B Whole Cube Formula

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Frequently Asked Questions on A minus B Whole Cube Formula

A-B Whole Cube Formula is one of the algebraic identities which is used to find the cube of a binomial. a-b whole cube formula can be written as follows 

(a - b)3 = a3 - 3ab(a-b) - b3