1. a) (b -9)² =b² -18b +81
b) (7 +6a)² =49 +84a -36a²
в) (4c -y)(4c +y) =16c² -y²
2. a) 3p² -12p -(p² -4) =3p² -12p -p² +4 =2p² -12p +4 = 2(p² -6p +2)
b) c² -6c +9 -2c² +4c =9 -c² -2c
в) 10py +5(p -y)² =10py + 5(p² -2py +y²) =10py +5p² - 10py +5y² =5p² +5y² =5(p² +y²)
3. a) a² -25 =(a -5)(a +5)
b) 49y²-4a² =(7y-2a)(7y+2a)
в) x² -4ax +4a² =(x -2a)²
г) 36c^3 -c =c(36c² -1) = c(6c -1)(6c +1)
4. (5a^3 +2)² -(5a^3 -2)² =
(5a^3+2 -(5a^3-2))(5a^3+2 +(5a^3-2)) =(5a^3+2 -5a^3 +2)(5a^3+2 +5a^3 -2) =
=4*10a^3 =40a^3
5.
178²+152² < 178²+ 2*178 * 152 +152²
6. 1 -2a² +a^4 =(1 -a²)² =
=(1 -a²)(1 -a²) =(1 -a)(1 +a)(1 -a)(1 +a)=(1 -a)²(1 +a)²