№5. Разложите на множители: 1) 25y2-4; 2) 36a²-60ab+25b2; 3) x³ - 8x2 + 16x; 4) ab5 - b5- ab³+b³;

№5. Разложим на множители:

1. $$25y^2 - 4 = (5y)^2 - 2^2 = (5y - 2)(5y + 2)$$
2. $$36a^2 - 60ab + 25b^2 = (6a)^2 - 2 \cdot 6a \cdot 5b + (5b)^2 = (6a - 5b)^2 = (6a - 5b)(6a - 5b)$$
3. $$x^3 - 8x^2 + 16x = x(x^2 - 8x + 16) = x(x^2 - 2 \cdot x \cdot 4 + 4^2) = x(x - 4)^2 = x(x - 4)(x - 4)$$
4. $$ab^5 - b^5 - ab^3 + b^3 = ab^5 - ab^3 - b^5 + b^3 = ab^3(b^2 - 1) - b^3(b^2 - 1) = (ab^3 - b^3)(b^2 - 1) = b^3(a - 1)(b - 1)(b + 1)$$

Ответ: 1) $$(5y - 2)(5y + 2)$$, 2) $$(6a - 5b)(6a - 5b)$$, 3) $$x(x - 4)(x - 4)$$, 4) $$b^3(a - 1)(b - 1)(b + 1)$$