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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. What is A+B Whole Cube formulas and Its use
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