Упростить выражения: 1) (y−2)(y+3)−(y−1)^2; 2) (c−5)(c−1)−(c−6)^2; 3) (p+1)^2−(p+2)^2; 4) (y−4)^2−(4−y)(4+y); 5) 4(a+5)^2−(4a^2+40a); 6) (4ab−b^2)+2(a−b)^2.

1. \((y-2)(y+3)-(y-1)^2=y^2+y-6-(y^2-2y+1)=3y-7\).
2. \((c-5)(c-1)-(c-6)^2=c^2-6c+5-(c^2-12c+36)=6c-31\).
3. \((p+1)^2-(p+2)^2=((p+1)-(p+2))((p+1)+(p+2))=-1\cdot(2p+3)=-2p-3\).
4. \((y-4)^2-(4-y)(4+y)=(y-4)^2-(16-y^2)=y^2-8y+16-16+y^2=2y^2-8y\).
5. \(4(a+5)^2-(4a^2+40a)=4(a^2+10a+25)-4a^2-40a=100\).
6. \((4ab-b^2)+2(a-b)^2=4ab-b^2+2(a^2-2ab+b^2)=2a^2+b^2\).

Ответ: 1) \(3y-7\); 2) \(6c-31\); 3) \(-2p-3\); 4) \(2y^2-8y\); 5) \(100\); 6) \(2a^2+b^2\).