Expanding (6m + 2)² using Pascal's Triangle
Pascal's Triangle is a powerful tool for expanding binomials, especially when dealing with higher powers. Let's explore how it helps us expand (6m + 2)².
Understanding Pascal's Triangle
Pascal's Triangle is a triangular array of numbers where each number is the sum of the two numbers directly above it. The first few rows of the triangle look like this:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
The rows of the triangle correspond to the power of the binomial we are expanding. For example, the 3rd row helps us expand (a + b)², the 4th row helps us expand (a + b)³, and so on.
Expanding (6m + 2)²
To expand (6m + 2)² using Pascal's Triangle, we need to consider the second row of the triangle, which is: 1 2 1. These numbers represent the coefficients for each term in our expansion.

Identify the terms: Our binomial is (6m + 2). Let's call 6m 'a' and 2 'b'.

Apply the coefficients:
 The first term is 1 * a² * b⁰ = 1 * (6m)² * 2⁰ = 36m²
 The second term is 2 * a¹ * b¹ = 2 * (6m)¹ * 2¹ = 24m
 The third term is 1 * a⁰ * b² = 1 * (6m)⁰ * 2² = 4

Combine the terms: Adding the terms together gives us the expanded form: (6m + 2)² = 36m² + 24m + 4
Conclusion
Using Pascal's Triangle simplifies the process of expanding binomials. By understanding the pattern and applying the coefficients, we can efficiently expand expressions like (6m + 2)² without having to perform lengthy multiplication.