Bài 1
a) M = (2a + b)² - (b - 2a)²
= (2a + b - b + 2a)(2a + b + b - 2a)
= 4a.2b
= 8ab
b) N = (3a + 2)² + 2(2 + 3a)(1 - 2b) + (2b - 1)²
= (3a + 2)² - 2(3a + 2)(2b - 1) + (2b - 1)²
= (3a + 2 - 2b + 1)²
= (3a - 2b + 3)²
Bài 2
a) (5 - 2x)² - 16 = 0
(5 - 2x)² - 4² = 0
(5 - 2x - 4)(5 - 2x + 4) = 0
(1 - 2x)(9 - 2x) = 0
1 - 2x = 0 hoặc 9 - 2x = 0
*) 1 - 2x = 0
2x = 1
x = 1/2
*) 9 - 2x = 0
2x = 9
x = 9/2
Vậy x = 1/2; x = 9/2
b) 5x(x - 3) - x + 3 = 0
5x(x - 3) - (x - 3) = 0
(x - 3)(5x - 1) = 0
x - 3 = 0 hoặc 5x - 1 = 0
*) x - 3 = 0
x = 3
*) 5x - 1 = 0
5x = 1
x = 1/5
Vậy x = 1/5; x = 3
Bài 3
a) 15x²y - 9x²y²
= 3x²y(5 - 3y)
b) x(x - 1) - y(1 - x)
= x(x - 1) + y(x - 1)
= (x - 1)(x + y)
