7) Use Pascal's Triangle to find the coefficients for (a + b)5 .
I need help with this?
5c0a^5 + 5c1a^4b + 5c2 a^3 b^2 + 5c3 a^2b^3 + 5c4ab^4 + 5c5b^5
5c0= 1= 5c5. . 5c1= 5 = 5c4 5c2= 10
5c3= 10
Plugging in these values,
a^5+ 5a^4b+ 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5
Sure, I can help you with that!
Pascal's Triangle is a triangular arrangement of numbers in which each number is the sum of the two numbers directly above it. To find the coefficients for (a + b)^5 using Pascal's Triangle, you need to look at the 6th row of the triangle (counting the topmost row as the 0th row).
Here's what the first few rows of Pascal's Triangle look like:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
To find the coefficients for (a + b)^5, we need to consider the 6th row of the triangle. Each number in this row represents the coefficient of the corresponding term in the expansion of (a + b)^5. In this case, the 6th row of Pascal's Triangle is:
1 5 10 10 5 1
Therefore, the coefficients of (a + b)^5 are 1, 5, 10, 10, 5, and 1 from left to right. This means that the expansion of (a + b)^5 can be written as:
1(a^5)(b^0) + 5(a^4)(b^1) + 10(a^3)(b^2) + 10(a^2)(b^3) + 5(a^1)(b^4) + 1(a^0)(b^5)
I hope this explanation helps! Let me know if you have any further questions.