1.
1) 14xy²z = 7*2xy²z = 2z
21x³y⁶ 7*3x³y⁶ 3x²y⁴
2) a(25-c²) = -a(c-5)(c+5) = -a(c+5) = -ac-5a
b(c-5) b(c-5) b b
3) 2b+18 = 2 (b+9) = 2
b²+18b+81 (b+9)² b+9
4) 4-y² = -(y-2)(y+2) =-(y+2) = y+2
y²-4y+4 (y-2)² y-2 2-y
2.
1) a²+3 - 3-a = 3(a²+3) - a²(3-a) = 3a²+9-3a²+a³ = 9+a³
a³ 3a 3a³ 3a³ 3a³
2) 15b-2 + 5+b = b(15b-2)+2(5+b)= 15b²-2b+10+2b = 15b²+10 = 5(3b²+2) =
10b² 5b³ 10b³ 10b³ 10b³ 10b³
=3b²+2
2b³
3) x-3 - x²-x = (x-3)(x+2)-(x²-x) = x²-3x+2x-6-x²+x = -6
x+2 x+2 x+2 x+2
4) x - 4y² = x - 4y² = x² -4y² = (x-2y)(x+2y) = x+2y
x-2y x² -2xy x-2y x(x-2y) x(x-2y) x(x-2y) x
5) x² + 1 = x² - 1 = x² - 1 =
x³-x 2-2x x(x²-1) 2(x-1) x(x-1)(x+1) 2(x-1)
= 2x² - x(x+1) = x(2x - (x+1)) = 2x-x-1 = x-1 =
2x(x-1)(x+1) 2x(x-1)(x+1) 2(x-1)(x+1) 2(x-1)(x+1)
= 1 = 1
2(x+1) 2x+2
6) 3 + 3 + 2x = 3 + 3 - 2x =
x+3 x²-3x 9-x² x+3 x(x-3) (x-3)(x+3)
= 3x(x-3)+3(x+3)-2x*x = 3x²-9x+3x+9-2x² = x²-6x+9 =
x(x-3)(x+3) x(x-3)(x+3) x(x-3)(x+3)
= (x-3)² = x-3 = x-3
x(x-3)(x+3) x(x+3) x²+3x
3.
36a²-b² = (6a-b)(6a+b) = 6a-b
36a²+12ab+b² (6a+b)² 6a+b
6*(-9) - 34 = -54-34 = -88 = 4.4
6*(-9)+34 -54+34 -20