A common way to simplify this problem would be to use an area model, or the distributive property. Using the distributive property does not require any drawing, so here goes.
(x-3)(x²+7x-8) Distribute by multiplying each of the terms in the first set of parentheses by every term in the second set of parentheses.
x³+7x³-8x-3x²-21x+24 Then combine alike terms.
8x³-3x²-29x+24 Is your final answer.