Multiply

1)8t^2(t-t^2+7t^3)

My Answer: 8t^3+-8t^4+56t

The first two terms are correct in your answer but the exponent for last term is wrong. When you are multiplying the exponents are added. So t^2.t^3 = t^(2+3) = t^5

so answer will be:
8t^3 - 8t^4 + 56t^5