(a+b)^2 Formula
The (a + b)2 formula is used to find the square of a binomial. This formula is also used to factorize some special types of trinomials. This formula is one of the algebraic identities. The (a + b)2 formula is the formula for the square of the sum of two terms. The (a + b)2 formula is widely used to factorize the binomial. The (a + b)2 formula is explained below along with solved examples in the following section.
What is (a+b)^2 Formula?
The (a + b)2 formula is the algebraic identity used to find the square of the sum of two numbers. To find the formula of of the binomial in the form (a + b)2, we will just multiply (a + b) (a + b).
(a + b)2= (a + b)(a + b)
= a2 + ab + ba + b2
= a2 + 2ab + b2
Therefore, (a + b)2 formula is:
(a + b)2 = a2 + 2ab + b2
You can understand this formula geometrically using the following figure:
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Example 1: Find the value of (3x + 2y)2 using (a + b)2 formula.
Solution:
To find: The value of (3x + 2y)2.
Let us assume that a = 3x and b = 2y.
We will substitute these values in (a + b)2 formula:
(a + b)2 = a2 + 2ab + b2
(3x+2y)2 =(3x)2 + 2(3x)(2y) +(2y)2
= 9x2+12xy+4y2
Answer: (3x + 2y)2 = 9x2 + 12xy + 4y2.
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Example 2: Factorize x2 + 4xy + 4y2 using (a + b)2 formula.
Solution:
To factorize: x2 + 4xy + 4y2.
We can write the given expression as: (x)2 + 2 (x) (2y) + (2y)2.
Using (a + b)2 formula:
a2 + 2ab + b2 = (a + b)2
Substitute a = x and b = 2y in this formula:
(x)2 + 2 (x) (2y) + (2y)2. = (x + 2y)2
Answer: x2 + 4xy + 4y2 = (x + 2y)2.