Can someone please tell me whether these are correct / how to fix them if they aren't?

(a) (a-b)^8

= a^8 - 8a^7b - 28a^6b^2 - 56a^5b^3 - 70a^4b^4 - 56a^3b^5 - 28a^2b^6 - 8ab^7 + b^8

(b) (3-2x)^8

= 3^8 - 8*3^7*2x - 28*3^6*2x^2 - 56*3^5*2x^3 - 70*3^4*2x^4 - 56*3^3*2x^5 - 28*3^2*2x^6 - 8*3*2x^7 + 2x^8
= 6561 - 34992x - 40824x^2 - 27216x^3 - 11340x^4 - 3024x^5 - 504x^6 - 48x^7 + 2x^8

Close, but you have a couple of mistakes. In the first expression, you got all of the coefficients right, but many of the signs are wrong. If it was (a+b)^8, all the coefficients would be positive, of course. Since there's a negative sign in front of the b, however, all the terms with odd powers of b will be negative. Hence it would be a^8-8a^7b+28a^6b^2-56a^5b^3+70a^4b^4-....

In the second case, you have the same issue with the signs, plus you also have to make sure you include the 2 when raising 2x to various powers. Hence, it should be (2x)^3=8x^3, for example.

Close, but you have a couple of mistakes. In the first expression, you got all of the coefficients right, but many of the signs are wrong. If it was (a+b)^8, all the coefficients would be positive, of course. Since there's a negative sign in front of the b, however, all the terms with odd powers of b will be negative. Hence it would be a^8-8a^7b+28a^6b^2-56a^5b^3+70a^4b^4-....

In the second case, you have the same issue with the signs, plus you also have to make sure you include the 2 when raising 2x to various powers. Hence, it should be (2x)^3=8x^3, for example.

Thanks! That was very helpful.

Thanks! That was very helpful.

You're welcome!