Question

Which of the following statements regarding Pascal's Triangle are correct?

A. The nth row gives the coefficients in the expansion of (x+y)^(n-1).

B. The method for generating Pascal's triangle consists of adding adjacent terms on the preceding row to determine the term below them.

C. Pascal's triangle can be used to expand binomials with positive terms only.

D. The nth row gives the coefficients in the expansion of (x+y)^n.

Answer 1

The correct statements regarding Pascal's Triangle are B and D, where B explains the method of forming Pascal's Triangle by adding adjacent terms and D states that the nth row gives the coefficients in the expansion of (x+y)^n.

Step-by-step explanation:

Among the given statements about Pascal's Triangle, options A and C are incorrect, whereas options B and D are correct. Here's why:

• B. The method for generating Pascal's triangle consists of adding adjacent terms on the preceding row to determine the term below them. This is a correct statement. Each number in Pascal's Triangle is the sum of the two numbers diagonally above it in the previous row.
• D. The nth row gives the coefficients in the expansion of (x+y)^n. This is accurate. If we consider the expansion of binomials using the Binomial theorem, the coefficients match the numbers in the nth row of Pascal's Triangle for the respective power of n.

Contrarily, options A and C contain misconceptions:

• A. The nth row gives the coefficients for the expansion of (x+y)^n, not (x+y)^(n-1).
• C. Pascal's Triangle can be used to find coefficients in the expansion of binomials with any real number terms, not just positive terms.

Answer 2

Statement A is incorrect, while statements B and D are correct regarding Pascal's Triangle.

Step-by-step explanation:

Statement A is incorrect. The nth row of Pascal's Triangle gives the coefficients in the expansion of (x+y)n, not (x+y)n-1.

Statement B is correct. The method for generating Pascal's Triangle is to add adjacent terms on the preceding row to determine the term below them.

Statement C is incorrect. Pascal's Triangle can be used to expand binomials with both positive and negative terms.

Statement D is correct. The nth row of Pascal's Triangle gives the coefficients in the expansion of (x+y)n.