Solving (x+3)(x+3) using the Identity (a+b)²
In mathematics, we often encounter expressions like (x+3)(x+3) that can be simplified using algebraic identities. One such identity that can be used to simplify this expression is (a+b)² = a² + 2ab + b².
Let's break down how to solve this problem using the identity:

Identify the values of 'a' and 'b': In our expression, (x+3)(x+3), we have:
 a = x
 b = 3

Apply the identity: Substitute the values of 'a' and 'b' into the identity: (a+b)² = a² + 2ab + b² (x+3)² = x² + 2(x)(3) + 3²

Simplify the expression: (x+3)² = x² + 6x + 9
Therefore, the simplified form of (x+3)(x+3) using the identity (a+b)² is x² + 6x + 9.
Why use the identity?
Using the identity (a+b)² directly simplifies the process of multiplying the expression. Instead of expanding it by using the distributive property, we can directly apply the identity to get the simplified result. This saves time and effort, especially when dealing with more complex expressions.
In conclusion, understanding and applying algebraic identities like (a+b)² can significantly streamline our mathematical calculations and help us arrive at solutions more efficiently.