The coefficients corresponding to k = 0, 1, 2, ..., 4 in the expansion of (x+y) ^4 are what

1, 4, 6, 4, 1

Step-by-step explanation:

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The coefficients in increasing order of k are;

1, 4, 6, 4, 1

Step-by-step explanation:

The expansion of (x+y) ^4 falls under the category of binomial expansions in which the coefficients are computed using combinations;

For k = 0, the coefficient is;

4 combination 0 = 1

For k = 1, the coefficient is;

4 combination 1 = 4

For k = 2, the coefficient is;

4 combination 2 = 6

For k = 3, the coefficient is;

4 combination 3 = 4

For k = 4, the coefficient is;

4 combination 4 = 1

These values can also be obtained from the Pascal's triangle;

The coefficients always exhibit some degree of symmetry