What is the A-B whole Square formula?
The algebraic identity is used to find the square of the difference between the two terms and is sometimes used to factorise the binomials.
(a - b)2 = a2 - 2ab - b2
(a - b)2 Formula Explanation and its Use
Basics: - This (a-b)2 formula is one of the algebraic identities that is used to find the square of a binomial. This (a-b)2 formula is used to find the square of the difference of the two terms. The (a-b)2 formula is called identity as this formula is valid for every value of 'a' and 'b'. The (a-b)2 formula is used to factorise the binomial. The explanations with examples of the formula (a-b)2 are given below.
The algebraic identity is used to find the square of the difference between the two terms and is sometimes used to factorise the binomials.
To find the formula, we will first write
(a - b)2= (a - b)(a - b)
By using binomial multiplication
(a - b)2 = a2 - ab - ba + b2
(a - b)2 = a2 - 2ab + b2
Therefore, (a - b)2 = a2 - 2ab - b2
Examples based on the (a-b)2 Formula are given below
Example 1: Find the value of (7x - 3y)2 by using the (a - b)2 formula.
Solution:
To find the value of (7x - 3y)2.
Let us assume that a = 7x and b = 3y.
Substitute these values of a and b in (a - b)2 formula:
=(a - b)2 = a2 - 2ab + b2
=(7x-3y)2 = (7x)2 - 2(7x) (3y) + (3y)2
= 49x2 - 42xy + 9y2
Answer: (7x - 3y)2 = 49x2 - 42xy + 9y2
Example 2: Factorize x2 - 6xy + 9y2 by using the (a - b)2formula.
Solution:
To factorize: x2 - 6xy + 9y2.
We can write the given expression as:
x2 - 6xy + 9y2 = (x)2 - 2 (x) (3y) + (3y)2.
Using (a - b)2 formula:
a2 - 2ab + b2 = (a - b)2
Substitute a = x and b = 3y in this formula:
(x)2 - 2 (x) (3y) + (3y)2 = (x - 3y)2
Answer:
x2 - 6xy + 9y2 = (x - 3y)2.
Example 3: Find the value of (30 - 5)2 using the (a - b)2 formula.
To find: (30-5)2
Let us assume that a = 30 and b = 5.
We will substitute these values in the formula of (a - b)2.
(a - b)2 = a2 - 2ab + b2
(30-5)2 = 900 - 2(30)(5) + 25
=900 - 300 + 25
=625
Answer: (30 - 5)2 = 625.
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FAQs for What is the A − B Whole Square Formula
The A − B Whole Square Formula is an algebraic identity used to expand the square of two terms connected by subtraction. The formula is:
(a - b)2 = a2 - 2ab - b2
This formula means that when a binomial is squared, the result contains three parts: the square of the first term, minus twice the product of both terms, and the square of the second term. It is widely used in algebra, simplification, factorisation, and solving equations. Students use this identity in school mathematics to solve numerical problems quickly and accurately. It also helps improve mental calculation skills and understanding of algebraic expressions in higher mathematics topics.
The A − B Whole Square Formula helps simplify multiplication problems involving squared expressions. For example, to solve ((x-5)^2), students can directly apply the identity instead of multiplying repeatedly. Using the formula gives:
((x-5)^2 = (x^2 - 10x + 25)
This method saves time and reduces mistakes in algebraic calculations. The formula is commonly used in polynomial expansion, coordinate geometry, and competitive exams. It is also useful in mental maths when calculating the squares of numbers near a base value. Understanding each term carefully helps students apply the identity correctly in both simple and advanced mathematical problems while improving overall problem-solving speed and accuracy.
The A − B Whole Square Formula is important because it forms the foundation of many algebraic concepts. It helps students understand polynomial expansion, identities, and simplification techniques. The formula is frequently used in equations, factorisation, quadratic expressions, and geometry-related calculations. Learning this identity improves logical thinking and mathematical accuracy. It is also useful in higher-level topics such as calculus and coordinate geometry. Many entrance and competitive examinations include questions based on algebraic identities, making this formula essential for practice. By mastering it, students can solve mathematical expressions faster and develop confidence in handling algebra problems efficiently.