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 Formula Explanation and its Use
Basics: - This (a-b)2 formula is one of the algebraic identities which 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 factorize 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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. What Is the (a - b)2 Formula in Algebra?
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)
(a - b)2 = a2 - 2ab - b2