№5. Разложите на множители: 1) 25y²-4; 2) 36a²-60ab+256²; 3) x38x2 + 16x; 4) ab5-b5-ab³+b³;

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