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

Get the List of Maths formulas. 

Find pdf of A-B Whole Cube Formula with solved example