145. Разложите на множители: 1) x² + 2xy + y² - 64; 2) m² + 16n² + 8mn - b²; 3) x³y + xy - y - y³; 4) a⁶ + 27 - 8a³ - a³; 5) x¹⁰ - 6x⁶ + 9x² - 36; 6) b⁴ + 64a⁴ + b² + 8ba + 16a²; 7) x² - 6xy + y² - a² - 2a - 1; 8) 4x² - y² - 4x + 1.

1) $$x^2 + 2xy + y^2 - 64 = (x + y)^2 - 8^2 = (x + y - 8)(x + y + 8)$$ 2) $$m^2 + 16n^2 + 8mn - b^2 = (m + 4n)^2 - b^2 = (m + 4n - b)(m + 4n + b)$$ 3) $$x^3y + xy - y - y^3 = xy(x^2 + 1) - y(1 + y^2) = y(x(x^2+1) - (1+y^2))$$ 4) $$a^6 + 27 - 8a^3 - a^3 = a^6-9a^3 + 27 = (a^2-3)(a^4+3a^2+9)$$ 5) $$x^{10} - 6x^6 + 9x^2 - 36 = x^6(x^4-6) + 9(x^2 - 4)$$ 6) $$b^4 + 64a^4 + b^2 + 8ba + 16a^2 = b^4 +b^2 + 8ab + 16a^2 +64a^4$$ 7) $$x^2 - 6xy + y^2 - a^2 - 2a - 1 = x^2 - 6xy + y^2 - (a^2 + 2a + 1) = x^2-6xy+y^2 - (a+1)^2$$ 8) $$4x^2 - y^2 - 4x + 1 = 4x^2 - 4x + 1 - y^2 = (2x - 1)^2 - y^2 = (2x - 1 - y)(2x - 1 + y)$$