Ответ:
№1.
а) (a-2)(a+2)-2a(5-a) = a^2-4-10a+2a^2 = 3a^2-4-10a = 3a^2-10a-4.
б) (y-9)^2-3y(y+1) = y^2-18y+81-3y^2-3y.
в) 3(x-4)^2-3x^2 = 3((x-4)^2-x^2) = 3(-4(x-4+x)) = 3(-4(2x-4)) = 3(-4*2(x-2)) = - 3*4*2(x-2) = -24(x-2).
№2.
а) 25x-x^3 = x(25-x^2) = x(5-x)(5+x).
б) 2x^2-20xy+50y^2 = 2(x^2-10xy+25y^2) = 2(x-5y)^2.
№3.
(c^2-b)^2-(c^2-1)(c^2+1)+2bc^2 = (c^4-2bc^2+b^2)(c^4-1)+2bc^2 = c^8-c^4-2bc^6+2bc^2+b^2c^4-b^2+2bc^2 = c^8-c^4-2bc^6+2bc^2+b^2c^4+2bc^2 = c^8-c^4-2bc^6+4bc^2+b^2c^4-b^2.
№4.
а) (x-3)^2-25x^2 = (x-3-5x)(x-3+5x) = (-4x-3)(6x-3) = (-4x-3)*3(2x-1) = 3(-4x-3)(2x-1).
б) a^2-b^2-4b-4a = (a-b)(a+b)-4(a+b) = (a+b)(a-b-4).
в) 8-y^6 = 2^3-y^3*2 = 2^3-(y^2)^3 = (2-y^2)(2^2+2y^2+(y^2)^2) = (2-y^2)*(4+2y^2+y^4).
№5.
(a+b)^2-(a-b)^2=4ab = a^2+2ab+b^2-a^2+2ab-b^2=4ab.