Expanding (x+3)(x+3) using the Identity
In mathematics, we often encounter expressions like (x+3)(x+3) that need to be simplified. We can use a handy algebraic identity to solve this quickly and efficiently.
What is the Identity?
The identity we will use is: (a + b)² = a² + 2ab + b²
This identity states that squaring a binomial (a + b) is equivalent to the sum of the square of the first term (a²), twice the product of the two terms (2ab), and the square of the second term (b²).
Applying the Identity to (x+3)(x+3)

Identify a and b: In our expression (x+3)(x+3), we have a = x and b = 3.

Substitute into the Identity: Substitute the values of a and b into the identity: (x + 3)² = x² + 2(x)(3) + 3²

Simplify: Simplify the expression: (x + 3)² = x² + 6x + 9
The Result
Therefore, using the identity (a + b)² = a² + 2ab + b², we find that (x+3)(x+3) = x² + 6x + 9.
Why use the Identity?
Using the identity provides a quick and efficient way to expand the expression. Instead of manually multiplying each term in the binomial, we can directly apply the identity to arrive at the simplified form.
This is particularly helpful when dealing with complex binomials or when repeated expansions are required.