bài 1.

B = (x - 2y)2 - (x + 2y)2 + (4y +1)(1 - 4y)

= (x - 2y - x - 2y)(x - 2y + x + 2y) + (1 + 4y)(1 - 4y)

= -4y.2x + 1 - 16y

= -8xy + 1 - 16y

E = (2x - 3)3 - (3x + 1)2 - 5(x - 2)(x + 2)

= (2x - 3 - 3x - 1)(2x - 3 + 3x +1) - 5(x2 - 4)

= (-x - 4).(5x -2) - 5x2 + 20

= -5x2 + 2x - 20x + 8 - 5x2 +20

= -10x2 - 18x + 28

bài 2

a) x2 - 6x + 8

= x2 - 2x - 4x + 8

= (x2 - 2x) - (4x - 8)

= x(x - 2) - 4(x - 2)

= (x - 4)(x - 2)

b) x2 + x - 2

= (x2 - x) + (2x - 2)

= x(x - 1) + 2(x - 1)

=(x + 2)(x - 1)

c) x3 - x2y - xy2 + y3

= (x3 - x2y) - (xy2 - y3)

= x2(x - y) - y2(x - y)

= (x2 - y2)(x - y)

bài 3

a) x2 - 81 = 0

(x - 9)(x + 9) = 0

=> x - 9 = 0 hoặc x + 9 = 0

=> x = 9 => x = -9

vậy x = 9 hoặc x = -9

b) x2 - x - 6 = 0

(x2 - 3x) + (2x - 6) = 0

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

=> x + 2 = 0 hoặc x - 3 = 0

=> x = -2 => x = 3

vậy x = -2 hoặc x = 3

c) x3 - 3x2 - x + 3 = 0

x3 - x - 3x2 + 3 = 0

(x3 - x) - (3x2 - 3) = 0

x(x2 - 1) - 3(x2 - 1) = 0

(x - 3)(x2 - 1) = 0

=> x - 3 = 0 hoặc x2 - 1 = 0

=> x = 3 => x2 = 1

=> x = 1

vậy x = 3 hoặc x = 1

d) 2(x + 3) - x2 - 3x = 0

2(x + 3) - (x2 + 3x) = 0

2(x + 3) - x(x + 3) = 0

(2 - x)(x + 3) = 0

=> 2 - x = 0 hoặc x + 3 = 0

=> x = 2 => x = -3

vậy x = 2 hoặc x = -3