Làm tính nhân: (2×2 – 3x)(5×2 – 2x + 1)

(x – 2y)(3xy + 5y2 + x)

= x.(3xy + 5y2 + x) + (-2y).(3xy + 5y2 + x)

= x.3xy + x.5y2 + x.x + (-2y).3xy + (–2y).5y2 + (–2y).x

= 3x2y + 5xy2 + x2 – 6xy2 – 10y3 – 2xy

= 3x2y + (5xy2 – 6xy2) + x2 – 10y3 – 2xy

= 3x2y – xy2 + x2 – 10y3 – 2xy

M = x2 + 4y2 – 4xy

= x2 – 2.x.2y + (2y)2 (Hằng đẳng thức (2))

= (x – 2y)2

Thay x = 18, y = 4 ta được:

M = (18 – 2.4)2 = 102 = 100

N = 8x3 – 12x2y + 6xy2 – y3

= (2x)3 – 3(2x)2y + 3.2xy2 – y3 (Hằng đẳng thức (5))

= (2x – y)3

Thay x = 6, y = - 8 ta được:

N = (2.6 – (-8))3 = 203 = 8000

(x + 2)(x – 2) – (x – 3)(x + 1)

= x2 – 22 – (x2 + x – 3x – 3)

= x2 – 4 – x2 – x + 3x + 3

= 2x – 1

(2x + 1)2 + (3x – 1)2 + 2(2x + 1)(3x – 1)

= (2x + 1)2 + 2.(2x + 1)(3x – 1) + (3x – 1)2

= [(2x + 1) + (3x – 1)]2

= (2x + 1 + 3x – 1)2

= (5x)2

= 25x2