1) b+4 - 3 =b+4-3b = 4-2b = -2(b-2) = -2
b(b-2) b-2 b(b-2) b(b-2) b(b-2) b
2) 1 - x+2 = 1 - x+2 = 3x-x-2 = 2x-2 = 2(x-1) = 2
x-1 3x²-3x x-1 3x(x-1) 3x(x-1) 3x(x-1) 3x(x-1) 3x
3) a² - a = a² - a = a²-a(a+7) = a²-a²-7a = -7a
a²-49 a-7 (a-7)(a+7) a-7 (a-7)(a+7) (a-7)(a+7) a²-49
4) x+1 + x = x+1 - x =(x+1)(1+x)-x*x =x²+2x+1-x² = 2x+1 =
x-x² x²-1 x(1-x) (1-x)(1+x) x(1-x)(1+x) x(1-x)(1+x) x(1-x²)
= 2x+1
x-x³
5) 2x² - 2x=2x²-2x(x-1) =2x²-2x²+2x= 2x
x-1 x-1 x-1 x-1
6) 1 - 1 + 4x = 1 - 1 + 4x =2x+y-2x+y+4x =
2x-y 2x+y 4x²-y² 2x-y 2x+y (2x-y)(2x+y) (2x-y)(2x+y)
=4x+2y
4x²-y²
7) a²+b² + b + b = a²+b² + b - b = a²+b²+b(a-b)-b(a+b) =
a²-b² a+b b-a (a-b)(a+b) a+b a-b (a+b)(a-b)
=a²+b²+ab-b²-ab-b²=a²-b² = 1
(a+b)(a-b) a²-b²
8) 3y+18 + 15y+57 - 2 = 3(y+6) + 15y+57 - 2 =
y²+12y+36 7y+42 (y+6)² 7(y+6)
= 3 + 15y+57 - 2= 7*3+15y+57-2*7(y+6) =21+15y+57-14y-84 =
y+6 7(y+6) 7(y+6) 7(y+6)
= y-6
7(y+6)
9) x+3 + 12 =x+3 + 12 = -x-3 + 12 =
x²-3x 9-x² x(x-3) (3-x)(3+x) x(3-x) (3-x)(3+x)
=-(x+3)(3+x) +12x =12x-x²-6x-9 = -x²+6x-9 =-(x²-6x+9) =
x(3-x)(3+x) x(3-x)(3+x) x(3-x)(3+x) x(3-x)(3+x)
= - (3-x)² = -(3-x) = x-3
x(3-x)(3+x) x(3+x) x²+3x