№2
а) Можно вынести общий множитель:
(2х+3) (2х-1) - (2х+1)(2х-1) = (2х-1)( 2х+3-2х-1) = (2х+1) *2=4х+2
или просто раскрыть скобки:
(2х+3)(2х-1) - (2х+1)(2х-1) = 4х² -2х+6х-3 - 4х²+1 =
= 4х +2
б) (3а-3b)² -3 (a-b)² = 9a²-18ab +9b²- 3 (a²-2ab+b²) =
= 9a²-18ab +9b²-3a²+6ab -3b²= 6a²-12ab+6b²=
= 6(a²-2ab +b²) = 6(a-b)²
в) (3х+1)(х-1) - (3х-1)(3х+1) = (3х+1)(х-1-3х+1) =
= (3х+1) * (-2х) = -6х²-2х
или
(3х+1)(х-1) - (3х-1)(3х+1) = 3х²-3х +х-1 -(9х²-1)=
= 3х²-2х-1-9х²+1= -6х²-2х
г) (2а+2b)²-2(a+b)²= 4a²+8ab +4b²-2a²-4ab-2b²=
= 2a²+4ab+2b² = 2 (a²+2ab+b²) = 2(a+b)²
№3
(а²+4)²-16а² = (а+2)² (a-2)²
a⁴+8a²+16 -16a² = (a+2)²(a-2)²
a⁴-8a²+16 = (a²-4)²
(a²)² -2*4a²+4² =(a²-4)²
(a²-4)² = (a²-4)²
б)
(4a+1)²(4a-1)² = (16a²+1)² -64a²
(16a²-1)² = (16a²) ² +32a²+1 -64a²
(16a²-1)² = (16a²)² - 2*16a² +1
(16a²-1)² = ( 16a²-1)²