(x^2 - 1).(x + 2) - (x - 2) (x^2 + 2x + 4)

= x^3 + 2x^2 - x - 2 - x^3 + 2^3

= 2x^2 - x - 2 + 8

= 2x^2 - x + 6

= 2x^2 - 4x + 3x + 6

= (2x^2 - 4x) - (3x - 6)

= 2x ( x - 2) - 3 (x - 2)

= (x - 2) (2x - 3)

(2x + 3)^2 - 2 (2x + 3) (2x + 5) + (2x + 5)^2

= [(2x + 3) - (2x + 5)]^2

= (2x + 3 - 2x - 5)^2

= -2^2

= 4

B = (3x + 2)^2 + (2x - 7)^2 - 2 (3x + 2) (2x - 7)

B = (3x + 2)^2 - 2 (3x + 2) (2x - 7) + (2x - 7)^2

B = [(3x + 2) - (2x - 7)]^2

B = (3x + 2 - 2x + 7)^2

B = (x + 9)^2

Thay x = -1/5 vào biểu thức:

B = (-1/5 + 9)^2

B = (44/5)^2

B = 1936/25

Bài 6:

a) 15x^3 y^2 + 10x^2 y^2 - 25x^2 y^3

= 5x^2 y^2 (3x + 2 - 5y)

b) x (x - 4) - 3y (4 - x)

= x (x - 4) + 3y (x - 4)

= (x - 4) (x + 3y)

c) 9x^2 + 6x + 1

= (3x)^2 + 2.3x.1 + 1^2

= (3x + 1)^2

d) 4x^2 - 9

= (2x)^2 - 3^2

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

e) x^3 + 27

= x^2 + 3^3

= (x + 3) (x^2 - 3x + 9)

f) 16x^2 - 9 (x + y)^2

= (4x)^2 - 3^2 (x + y)^2

= (4x)^2 - [3 (x + y)]^2

= (4x)^2 - (3x + 3y)^2

= [4x - (3x + 3y)] [4x + (3x + 3y)]

= (4x - 3x - 3y) (4x + 3x + 3y)

= (x - 3y) (7x + 3y)

g) x^2y + xy^2 - x - y

= (x^2y + xy^2) - (x + y)

= xy (x + y) - 1 (x + y)

= (x + y) (xy - 1)

h) x^2 + 2xy + y^2 -25

= (x^2 + 2xy + y^2) - 5^2

= (x + y)^2 - 5^2

= (x + y - 5) (x + y + 5)

i) 2x^2 - x - 6xy + 3y

= (2x^2 - x) - (6xy - 3y)

= x (2x -1) - 3y (2x -1)

= (2x - 1) (x - 3y)

(x^2 - 1).(x + 2) - (x - 2) (x^2 + 2x + 4)

= x^3 + 2x^2 - x - 2 - x^3 + 2^3

= 2x^2 - x - 2 + 8

= 2x^2 - x + 6

= 2x^2 - 4x + 3x + 6

= (2x^2 - 4x) - (3x - 6)

= 2x ( x - 2) - 3 (x - 2)

= (x - 2) (2x - 3)