a(x - y) + b(y - x)

Для решения этих выражений используем правило: $(x - y) = -(y - x)$ и $(x - y)^2 = (y - x)^2$. 1. $a(x - y) + b(y - x) = a(x - y) - b(x - y) = (x - y)(a - b)$ 2. $(x - y)^2 - p(y - x) = (x - y)^2 + p(x - y) = (x - y)(x - y + p)$ 3. $a(p - k) + b(k - p)^2 = a(p - k) + b(p - k)^2 = (p - k)(a + b(p - k)) = (p - k)(a + bp - bk)$ 4. $4(a - 2b)^2 - (2b - a) = 4(a - 2b)^2 + (a - 2b) = (a - 2b)(4(a - 2b) + 1) = (a - 2b)(4a - 8b + 1)$ 5. $x(a - b)^2 + y(b - a)^2 = x(a - b)^2 + y(a - b)^2 = (a - b)^2(x + y)$ 6. $x(a - b)^2 - y(b - a)^3 = x(a - b)^2 - y(-(a - b))^3 = x(a - b)^2 + y(a - b)^3 = (a - b)^2(x + y(a - b)) = (a - b)^2(x + ya - yb)$ 7. $5(x - y)^2 - 10(x - y) = 5(x - y)(x - y - 2)$ 8. $5(x - y) - 10(x - y)^2 = 5(x - y)(1 - 2(x - y)) = 5(x - y)(1 - 2x + 2y)$ 9. $8x(a - b) - 4x^2(a - b) = 4x(a - b)(2 - x)$ 10. $6x^2(a - b) + 9x(a - b) = 3x(a - b)(2x + 3)$