## Expanding (m + n)^6 using Pascal's Triangle

Pascal's Triangle is a powerful tool for expanding binomials raised to a power. It provides the coefficients for each term in the expansion. Let's see how to use it to expand (m + n)^6.

### 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 are:

```
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
```

**Key Observations:**

**Rows:**The rows are numbered starting from 0.**Coefficients:**The numbers in each row represent the coefficients in the expansion of (x + y)^n, where 'n' is the row number.**Symmetry:**The triangle is symmetrical, meaning the numbers on the left and right sides are the same.

### Expanding (m + n)^6

To expand (m + n)^6, we need the coefficients from the 6th row of Pascal's Triangle: **1 6 15 20 15 6 1**.

Now, follow these steps:

**Powers of m:**The powers of 'm' decrease from 6 to 0, starting with m^6.**Powers of n:**The powers of 'n' increase from 0 to 6, starting with n^0.**Coefficients:**Multiply each term by the corresponding coefficient from Pascal's Triangle.

Therefore, the expansion is:

**(m + n)^6 = 1m^6 + 6m^5n + 15m^4n^2 + 20m^3n^3 + 15m^2n^4 + 6mn^5 + 1n^6**

### Summary

Using Pascal's Triangle to expand binomials is a straightforward and efficient method. The triangle provides the coefficients, and you simply need to adjust the powers of the variables.