Pascal's Triangle is used to simplify the process of binomial expansion
The correct response:
- No. The values in Pascal's Triangle are the values of the coefficients in a binomial expansion.
Reasons why the above response is correct
Pascal's Triangle is an array of numbers arranged in a triangular pattern
that gives a binomial expansion coefficients.
Pascal's Triangle is presented in the form;
[tex]{}[/tex] 1
1 [tex]{}[/tex] 1
1 [tex]{}[/tex] 2 1
1 3 [tex]{}[/tex]3 1
1 [tex]{}[/tex] 4 6 4 1
1[tex]{}[/tex] 5 10 10 5 1
Therefore, we have;
(x + y)⁰ = 1
(x + y)¹ = x + y
(x + y)² = x² + 2·x·y + y²
(x + y)³ = x³ + 3·x²·y + 3·y²·x + y³
(x + y)⁴ = x⁴ + 4·x³·y + 6·x²·y² + 4·x·y³ + y⁴
(x + y)⁵ = x⁵ + 5·x⁴·y + 10·x³·y² + 10·x²·y³ + 5·x·y⁴ + y⁵
The coefficients of the above, binomial expansion corresponds to the
values on each row on the Pascal's Triangle.
Therefore;
Alby's statement that the numbers in Pascal's Triangle are the values of the
exponents on the variables in a binomial expansion, is not correct.
The correct option is therefore;
- No. The values in Pascal's Triangle are the values of the coefficients in a binomial expansion.
Learn more about Pascal's Triangle here:
https://brainly.com/question/9369434
