2) Представьте выражение в виде многочлена стандартного вида: a) (7x2 - 4x + 8) - (4x2 + x – 5); б) 5a(a4 – 6a² + 3); в) (x + 4)(3x - 2); г) ( x + 5)(x² + x − 6).

a) (7x² - 4x + 8) - (4x² + x - 5) = 7x² - 4x + 8 - 4x² - x + 5 = (7x² - 4x²) + (-4x - x) + (8 + 5) = 3x² - 5x + 13

б) 5a(a⁴ - 6a² + 3) = 5a ⋅ a⁴ - 5a ⋅ 6a² + 5a ⋅ 3 = 5a^(1+4) - 30a^(1+2) + 15a = 5a⁵ - 30a³ + 15a

в) (x + 4)(3x - 2) = x ⋅ 3x - x ⋅ 2 + 4 ⋅ 3x - 4 ⋅ 2 = 3x² - 2x + 12x - 8 = 3x² + 10x - 8

г) (x + 5)(x² + x - 6) = x ⋅ x² + x ⋅ x - x ⋅ 6 + 5 ⋅ x² + 5 ⋅ x - 5 ⋅ 6 = x³ + x² - 6x + 5x² + 5x - 30 = x³ + (x² + 5x²) + (-6x + 5x) - 30 = x³ + 6x² - x - 30

Ответ: a) 3x² - 5x + 13; б) 5a⁵ - 30a³ + 15a; в) 3x² + 10x - 8; г) x³ + 6x² - x - 30