Задание 1: 1) a²-a b = a(a - b) 2) 8m²n - 4mn³ = 4mn (2m – n²) 3) (a+b) -x (a+b) = 1(a+b)-x (a+b) = (a+b)(1-x) 3) x²m-x²n + y²m- y²n = (x

Решения заданий 1: 1) a²-ab = a(a-b) a² - ab = a² - ab 2) 8m²n - 4mn³ = 4mn(2m - n²) 8m²n - 4mn³ = 8m²n - 4mn³ 3) (a+b) - x(a+b) = (a+b) - x(a+b) = (a+b)(1-x) (a+b) - x(a+b) = (a+b)(1-x) (a+b)(1-x) = (a+b)(1-x) Задание 2: 1) ax + ay - x - y = (a-1)(x-y) ax + ay - x - y = (a-1)(x-y) a(x+y) - (x+y) = (a-1)(x-y) (a-1)(x+y) = (a-1)(x-y) - Ошибка! 2) ab - 8a - 6x + 8x = (b-8)(a-x) ab - 8a - 6x + 8x = (b-8)(a-x) - Ошибка! 3) x²m - x²n + y²m - y²n = (x-y)(x+y)(m-n) x²m - x²n + y²m - y²n = (x-y)(x+y)(m-n) x²(m-n) + y²(m-n) = (x-y)(x+y)(m-n) (x² + y²)(m-n) = (x-y)(x+y)(m-n) (x² + y²)(m-n) = (x² - y²)(m-n) - Ошибка! 4) 7a - 7b + an - bn = (a-b)(7+n) 7(a-b) + n(a-b) = (a-b)(7+n) (a-b)(7+n) = (a-b)(7+n) 5) xy + 2y + 2x + 4 = (x+2)(y+2) y(x+2) + 2(x+2) = (x+2)(y+2) (x+2)(y+2) = (x+2)(y+2) 6) y²a - y²b + x²a - x²b = (a-b)(y²+x²) a(y²+x²) - b(y²+x²) = (a-b)(y²+x²) (a-b)(y²+x²) = (a-b)(y²+x²) 7) xy + 2y - 2x - 4 = (x+2)(y-2) y(x+2) - 2(x+2) = (x+2)(y-2) (x+2)(y-2) = (x+2)(y-2) 8) 2cx - cy - 6x + 3y = (2x-y)(c-3) c(2x-y) - 3(2x-y) = (2x-y)(c-3) (2x-y)(c-3) = (2x-y)(c-3) 9) x² + x y + xy² + y³ = (x+y²)(x+y) x(x+y) + y²(x+y) = (x+y²)(x+y) (x+y)(x+y²) = (x+y)(x+y²) 10) x⁴ + x³y - xy³ - y⁴ = (x+y)(x³-y³)=(x+y)(x-y)(x²+xy+y²) x³(x+y) - y³(x+y) = (x+y)(x³-y³) (x+y)(x³-y³) = (x+y)(x³-y³) 11) xy² - by² - ax + ab + y² - a = (y²-a)(x-b+1) - Ошибка в условии! 12) x² - 5x + 6 = x² - 2x - 3x + 6 = (x-2)(x-3) x² - 5x + 6 = (x-2)(x-3) x² - 2x - 3x + 6 = (x-2)(x-3) x(x-2) - 3(x-2) = (x-2)(x-3) (x-2)(x-3) = (x-2)(x-3)