If we generalize this binomial expansion to any n-th power of (r+y), then we get, -(1)-....

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If we generalize this binomial expansion to any n-th power of (r+y), then we get, -(1)-. (a+y)" => which is called "binomial theorem." Problem 1 (4 Points) As an exercise, apply the binomial theorem to the expansion of (x+y) below. Your task is to fill in the blank line (3), involving the combinations (in the way it is written in (2) above for the expansion of (x + y)), and find the coefficient for each additive term in line (4) (in the way it is written in (1) above for the expansion of (x + y)³). (x+y) 4 Σ k=0) (3) Also, answer the following questions. Problem 2 (1 Point) What is the coefficient of the term zy2 in the expansion of (x + y) ? Problem 3 (1 Point) What is the coefficient of the term r²y in the expansion of (x + y)? Problem 4 (2 Points) What is the coefficient of the term ry in the expansion of (x + y)? Problem 5 (2 Points) List all the coefficients in the expansion of (x + y). For example, in the expansion of (x+y)³, the list of coefficients is [1, 3, 3, 1]. If we generalize this binomial expansion to any n-th power of (r+y), then we get, -(1)-. (a+y)" => which is called "binomial theorem." Problem 1 (4 Points) As an exercise, apply the binomial theorem to the expansion of (x+y) below. Your task is to fill in the blank line (3), involving the combinations (in the way it is written in (2) above for the expansion of (x + y)), and find the coefficient for each additive term in line (4) (in the way it is written in (1) above for the expansion of (x + y)³). (x+y) 4 Σ k=0) (3) Also, answer the following questions. Problem 2 (1 Point) What is the coefficient of the term zy2 in the expansion of (x + y) ? Problem 3 (1 Point) What is the coefficient of the term r²y in the expansion of (x + y)? Problem 4 (2 Points) What is the coefficient of the term ry in the expansion of (x + y)? Problem 5 (2 Points) List all the coefficients in the expansion of (x + y). For example, in the expansion of (x+y)³, the list of coefficients is [1, 3, 3, 1].