(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)
= a^{2} + ab + ba + b^{2}
= a^{2} + 2ab + b^{2}
Therefore, (a + b)^{2} formula is:
(a + b)^{2} = a^{2} + 2ab + b^{2}
You can understand this formula geometrically using the following figure:

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} = a^{2} + 2ab + b^{2}
(3x+2y)^{2} =(3x)^{2} + 2(3x)(2y) +(2y)^{2}
= 9x^{2}+12xy+4y^{2}
Answer: (3x + 2y)^{2} = 9x^{2} + 12xy + 4y^{2}.

Example 2: Factorize x^{2} + 4xy + 4y^{2} using (a + b)^{2} formula.
Solution:
To factorize: x^{2} + 4xy + 4y^{2}.
We can write the given expression as: (x)^{2} + 2 (x) (2y) + (2y)^{2}.
Using (a + b)^{2} formula:
a^{2} + 2ab + b^{2} = (a + b)^{2}
Substitute a = x and b = 2y in this formula:
(x)^{2} + 2 (x) (2y) + (2y)^{2}. = (x + 2y)^{2}
Answer: x^{2} + 4xy + 4y^{2} = (x + 2y)^{2}.