Find the coefficients of this binomial using Pascal’s triangle: (a + b)^8.
can you not look up Pascal's Triangle?
The nth term (starting from n=0) has C(8,n) as its coefficient
To find the coefficients of the binomial (a + b)^8 using Pascal's triangle, you need to look at the 8th row of 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 rows of Pascal’s triangle represent the coefficients of the binomial expansion.
So, let's take a look at the 8th row of Pascal’s triangle:
1 8 28 56 70 56 28 8 1
These numbers represent the coefficients of the expansion of (a + b)^8.
To understand how these coefficients are obtained, here's how you can expand (a + b)^8 using Pascal's triangle:
The expansion of (a + b)^8 can be written as:
1a^8 + 8a^7b^1 + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a^3b^5 + 28a^2b^6 + 8ab^7 + 1b^8
Each term in the expansion follows the pattern of using the coefficients from Pascal's triangle, in this case, the 8th row.
So, the coefficients of (a + b)^8 are:
1, 8, 28, 56, 70, 56, 28, 8, 1