A + B Whole Square Formula and Its Use
This (a+b)2 formula is one of the algebraic identities that is used to find the square of a binomial
The A Plus B Whole Square Formula is one of the most important algebraic identities used in school mathematics. It helps students solve algebraic expressions quickly, simplify calculations, and expand binomials easily. This Maths formula is widely used in algebra, polynomial expansion, and mental maths calculations from middle school to higher classes.
(a+b)2 Formula
(a+b)2 = a2+ 2ab + b2
Basics: This (a+b)2 formula is one of the algebraic identities that is used to find the square of a binomial. The (a+b)2 formula is used to find the square of the sum of two terms. The (a+b)2 formula is called an identity, as this formula is valid for every value of 'a' and 'b'. The 2 formulas are used to factorise the binomial. The explanations with examples of the formula (a+b)2 are given below.
Explanation of (a+b)2 Formula
The algebraic identity is used to find the square of 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 (3x + 7y)2 using (a + b)2 formula.
Solution:
To find: The value of (2x + 7y)2.
Let us assume that a = 2x and b = 7y.
(a + b)2 = a2 + 2ab + b2
(2x+3y)2 =(2x)2 + 2(2x)(7y) +(7y)2
= 4x2+28xy+49y2
Answer: (3x + 7y)2 = 4x2+ 28xy + 49y2.
Example 2: Factorize 4x2 + 4xy + y2 using (a + b)2 formula.
Solution:
To factorize: 4x2 + 4xy + y2.
The expression can be written as: (2x)2 + 2 (2x) (y) + (y)2.
a2 + 2ab + b2 = (a + b)2
Substitute a = 2x and b = y in this formula:
(2x)2 + 2 (2x) (y) + (y)2. = (2x + y)2
Answer: 4x2 + 4xy + y2 = (2x + y)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
= 1225
Answer: (30 + 5)2 = 1225
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FAQs for A Plus B Whole Square Formula
The A Plus B Whole Square Formula is an algebraic identity used to expand the square of two terms added together. The formula is:
(a+b)2 = a2+ 2ab + b2
In this identity, the first term is squared, the second term is squared, and the middle term is twice the product of both terms. This formula helps students solve algebraic expressions quickly and accurately. It is commonly used in polynomial expansion, simplification, and mental maths calculations. Students from classes 6 to 12 use this identity regularly in mathematics.
To solve questions using the formula, first identify the two terms inside the bracket. Then apply the identity step by step by squaring the first term, finding twice the product of both terms, and squaring the second term.
Example:
(x+4)2 =x2+2(x)(4)+42=x^2+2(x)(4)+4^2=x2+2(x)(4)+42 =x2+8x+16=x^2+8x+16=x2+8x+16
This method makes algebraic calculations easier and reduces mistakes during exams.
The formula is used in many areas of mathematics such as algebra, polynomial expansion, factorisation, coordinate geometry, and competitive exam preparation. It is also useful in mental maths for finding squares of numbers quickly. Students use this identity in school exams as well as higher mathematics topics because it simplifies lengthy calculations.
One common mistake is forgetting the middle term (2ab). Some students only square the first and second terms and miss the product term. Another mistake is incorrect sign handling during calculations. Students should carefully apply all three parts of the identity:
- Square of the first term
- Twice the product of both terms
- Square of the second term
Practising regularly helps improve accuracy and speed.