A plus B Whole Square
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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