Answer:

Yes, the expression (4p-2q+1)(16p² - 4p + 8pq - 4q + 4q² + 1) can still be simplified further using the distributive property.

Using the distributive property, we need to multiply each term in the first parentheses (4p-2q+1) by each term in the second parentheses (16p² - 4p + 8pq - 4q + 4q² + 1):

(4p-2q+1)(16p² - 4p + 8pq - 4q + 4q² + 1) =

(4p)(16p² - 4p + 8pq - 4q + 4q² + 1) - (2q)(16p² - 4p + 8pq - 4q + 4q² + 1) + (1)(16p² - 4p + 8pq - 4q + 4q² + 1)

Expanding and simplifying each term of the expression gives:

(4p)(16p²) + (4p)(-4p) + (4p)(8pq) + (4p)(-4q) + (4p)(4q²) + (4p)(1)

- (2q)(16p²) + (2q)(-4p) + (2q)(8pq) + (2q)(-4q) + (2q)(4q²) + (2q)(1)

+ (1)(16p²) + (1)(-4p) + (1)(8pq) + (1)(-4q) + (1)(4q²) + (1)(1)

Which simplifies to:

64p³ - 16p² + 32p²q - 16pq + 16pq² + 4p - 32p²q + 8pq - 16q² + 8q³ - 4q + 16p² - 4p + 8pq - 4q + 4q² + 1

By combining like terms, the expression simplifies further to:

8q³ + 64p³ + 8q² + 12pq + 1

So, the simplified form of the expression (4p-2q+1)(16p² - 4p + 8pq - 4q + 4q² + 1) is 8q³ + 64p³ + 8q² + 12pq + 1.