Find the coefficients of X^12y^6 in the expansion of (x^3-3y)^10

Find the constant term in the expansion of (y-1/2y)^10

Here is one way to go about it by listing out the terms.

The first term will be

The coefficient of the second term will be the exponent from the first term.



Reduce the exponents of x by 3 and add 1 to the exponent of y.

Now, To find the next coefficient, multiply the coefficient by the exponent and divide by 1 more than the exponent of y. 30*27/2=405

So, the next term is

The next would be 405*24/3=3240



Continue in this manner until you get to y^6. Not too much further.

So far, we have

Remember to alternate your signs.

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For the second one, is that ?

If so, look at it. It is just . Now, can you see the constant term?