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THIRTY POINTS PLEASE!
Alby says that the numbers in Pascal's Triangle are the values of the exponents on the variables in a binomial expansion. Is Alby correct?
No, the values in Pascal's Triangle represent the exponents on the a terms only.
No, the values in Pascal's Triangle represent the exponents on the b terms only.
No. The values in Pascal's Triangle are the values of the coefficients in a binomial expansion.
Yes, the values in Pascal's Triangle are the values of the exponents on the variables in a binomial expansion.

Sagot :

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

Answer:

No. The values in Pascal's Triangle are the values of the coefficients in a binomial expansion.

Step-by-step explanation:

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