1. a) 4x² +8x =4x(x +2)
b) 3m -6n +mn -2n² =(3m +mn) -(6n +2n²) =m(3 +n) - 2n(3 +n) =(3 +n)(m +2n)
в) 9a² -16 =(3a -4)(3a +4)
г) y^3 +18y² +81y=y(y² + 2*y*9 +9²) =y(y +9)² = y(y +9)(y +9)
2. a) (36 -a²) /(18 +3a) = (6 -a)(6 +a) /3(6 +a) =(6 -a) /3
b) (9p²-q²) /(9p²+6pq+q²) = (3p -q)(3p +q) /(3p +q)² = (3p -q) /(3p +q)
3. x² -36x =0
x(x -36) =0
x=0
x -36 =0
x =36
ответ: x=0, x=36
4. x² +14x +48 =(x+8)(x+6)
(x +8)(x +6) =x² +6x +8x +48 =x² +14x +48
(x +8)(x +6) =(x +8)(x +6)
5. 1) (169^3 +59^3) /228 = (169+59)*(169²-169*59+59²) / 228 =228(169² -169*59+ 59²) /228 =169² -169*59 + 59²
2)
169²-169*59 +59²-169*59 = 169² -2(169*59) +59² = (169 -59)² =(169 -59)(169 -59) = 110 *110 =12100