1. a) 5y(3y -2) -(y -1)(y +1) =15y² -10y -(y² -1) =15y² -10y -y² +1 =14y² -10y +1
б) (d -8)(d +4) +(d -5)² =d² -4d -32 +d² -10d +25 =2d² -14d -7
в) 6(c +d)² -12cd =6(c² +2cd +d²) -12cd =6c² +12cd +6d² -12cd =6c² +6d²
2. a) b^3 -36b =b(b² -36) =b(b -6)(b +6)
b) -2a² +8ab -8b² = -2(a² -4ab +4b²) = -2(a -2b)² = -2(a -2b)(a -2b)
3. (b+3)²(b -3) +3(b+3)(b -3) =(b+3)(b-3)(b+3 +3) =(b +3)(b -3)(b +6) =(-2 +3)(-2 -3)(-2 +6) =1*(-5)*4 = -20
4. a) (y -3)² -16y² =(y-3 -4y)(y-3 +4y) =(-3y -3)(5y -3) = -3(y +1)(5y -3)
b) x² -y² -y -x =(x² -y²) -(x +y) =(x -y)(x +y) -(x +y) =(x +y)(x -y -1)
5. a^4 -1 =(a² -1)(a² +1) =(a -1)(a +1)(a² +1) =(a -1)(a^3+a²+a+1)
(a -1)(a^3 +a² +a +1) =(a -1)(a^3 +a² +a +1)
что и требовалось доказать