A Plus B Whole Cube Formula

What is A+B Whole Cube Formula

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

(a+b)3 Formula

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 sum of 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= (a3 + 2ab + b3)(a + b)

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

(a+b)3 a3 + 3a2b + 3ab2 + b3

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

Therefore, (a+b)3 formula is:

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

Application and Examples of (a+b)3 Formula (Example of A plus B Whole Cube Formula)

Example 1: Expand (4a +5b)3

Solution

Putting 4a = x and 5b = y, we get (4a +5b)3 = (x+y)3

= x3+y3 + 3xy (x + y)

= (4a)3 + (5b)3 + (3 × 4a × 5b) (4a + 5b)

= 64a3 + 125b3 +60ab (4a +5b)

= 64a3+125b3 +240a2b + 300ab2.

Example 2: Factorise

(i) 8a3 + b3 +12a2b + 6ab2

Solution We have

(i) 8a3 + b3 +12a2b +6ab2

= (2a)3 + b3 +6ab (2a + b)

= (2a)3 + b3 +(3× 2a × b) (2a + b)

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

Example 3:

Evaluate (102)3 by using (a + b)3 Formula

(102)3 = (100+2) 3 3

= (100)3 +23+3× 100 × 2 × (100+2)

= 1000000+8+ (600 × 102)

= 1000008 +61200 = 1061208.

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A Plus B Whole Cube Formula
A Plus B Whole Cube Formula

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The A+B Whole Cube formula is frequently used in Maths algebra and its most common formula, students must remember what is A+B Whole Cube with the proper understanding of its use. A+B Whole Cube can be defined as (a+b)3= a3 + 3ab(a+b) + b3