To simplify the expression 4p²(p-2) - 3pp - 7pp*p - (p^3 - 3p), we need to first distribute the terms in the parentheses and then combine like terms.

Step 1: Distribute the terms inside the parentheses:
= 4p²(p) - 4p²(2) - 3pp - 7pp*p - p^3 + 3p

Step 2: Simplify each term:
= 4p³ - 8p² - 3p² - 7p³ - p³ + 3p

Step 3: Combine like terms:
= (4p³ - 7p³ - p³) + (-8p² - 3p²) + 3p
= -4p³ - 11p² + 3p

Therefore, the simplified expression is -4p³ - 11p² + 3p.