1) (2p-q)²+2q²-3pq = 4p²-4pq+q²+2q²-3pq = 4p²-7pq+3q² = 4p²-4pq-3pq+3q² =
= 4p(p-q)-3q(p-q) = (p-q)(4p-3q)
2) 2p⁻¹+q² = 2/p + q² = 2/p + pq²/p = 2+pq² / p
3) (p-q)(4p-3q) : 2+pq² / p = (p-q)(4p-3q) * p / 2+pq² = p(p-q)(4p-3q) / 2+pq²
4) 4p²-3pq = p(4p-3q)
5) p(p-q)(4p-3q) / 2+pq² : p(4p-3q) / 2+pq² = p(p-q)(4p-3q) / 2+pq² * 2+pq² / p(4p-3q) = p-q