A + B Whole Cube Formula
What is the A+B Whole Cube Formula
The A + B Whole Cube Formula is an important algebraic identity used to expand the cube of two terms added together. It is widely used in algebra, polynomial simplification, and higher mathematics. Students learn this identity to solve mathematical expressions quickly and accurately without performing lengthy multiplication steps.
The formula of A + B Whole Cube is: (a+b)3= a3 + 3ab(a+b) + b3
This identity shows that the cube of a sum contains four terms. The first and last terms are the cubes of each value, while the middle terms involve the multiplication of both values by coefficients. The formula is commonly used in school mathematics from middle school to higher secondary education. It helps students expand algebraic expressions, simplify equations, and solve polynomial problems easily. Questions based on this identity are frequently asked in exams and competitive tests.
This method saves time and improves calculation speed.
The A + B Whole Cube Formula is also useful in mental maths. Large number calculations can be simplified using this identity. It is applied in algebraic proofs, factorisation, coordinate geometry, and advanced mathematics topics. Students should remember all four terms carefully while applying the formula. A common mistake is forgetting the middle terms or using incorrect signs. Regular practice helps in understanding the pattern and solving questions faster. Overall, the A + B Whole Cube Formula is one of the most essential algebraic identities in mathematics and forms the foundation for many advanced concepts in higher classes.
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 that 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 an identity, as this formula is valid for every value of 'a' and 'b'. The (a+b)3 formula is used to factorise 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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