bx - by + px - py

Разложение многочленов на множители методом группировки: 1. $bx - by + px - py = b(x - y) + p(x - y) = (x - y)(b + p)$ 2. $3\alpha + b\alpha + 3m + bm = \alpha(3 + b) + m(3 + b) = (3 + b)(\alpha + m)$ 3. $2\alpha + pk + k\alpha + 2p = \alpha(2 + k) + p(k + 2) = (2 + k)(\alpha + p)$ 4. $3x + mn + nx + 3m = 3(x + m) + n(m + x) = (x + m)(3 + n)$ 5. $xy + xb - 4y - 4b = x(y + b) - 4(y + b) = (y + b)(x - 4)$ 6. $m\alpha + mb - 5\alpha - 5b = m(\alpha + b) - 5(\alpha + b) = (\alpha + b)(m - 5)$ 7. $6m + 6n - 4m - 4n = 2m + 2n = 2(m + n)$ 8. $3x + 5y + 15 + xy = 3(x + 5) + y(5 + x) = (x + 5)(3 + y)$ 9. $7m - 8n + 14m - 4n = 21m - 12n = 3(7m - 4n)$ 10. $\alpha b + 6 + 3b + 2\alpha = b(\alpha + 3) + 2(3 + \alpha) = (\alpha + 3)(b + 2)$ 11. $2xy + 27 + 3x + 18y = x(2y + 3) + 9(3 + 2y) = (2y + 3)(x + 9)$ 12. $25\alpha - 3b - 5\alpha b + 15 = 5\alpha(5 - b) + 3(5 - b) = (5 - b)(5\alpha + 3)$ 13. $4x - 24y + 8 - 12xy = 4(x - 6y + 2 - 3xy) = 4[x(1 - 3y) + 2(1 - 3y)] = 4(1 - 3y)(x + 2)$ 14. $30b + 20 - 12b\alpha - 8\alpha = 10(3b + 2) - 4\alpha(3b + 2) = (3b + 2)(10 - 4\alpha) = 2(3b + 2)(5 - 2\alpha)$ 15. $5c + 5c^2 + b + bc = 5c(1 + c) + b(1 + c) = (1 + c)(5c + b)$ 16. $8\alpha^2 + 20b\alpha - 6\alpha - 15b = 4\alpha(2\alpha + 5b) - 3(2\alpha + 5b) = (2\alpha + 5b)(4\alpha - 3)$ 17. $12\alpha^2 - 6b\alpha + 60\alpha - 30b = 6\alpha(2\alpha - b) + 30(2\alpha - b) = (2\alpha - b)(6\alpha + 30) = 6(2\alpha - b)(\alpha + 5)$ 18. $4x - 18xy + 12x^2 - 6y = 2(2x - 9xy + 6x^2 - 3y) = 2[2x(1 + 3x) - 3y(3 + 1)] = 2(1 + 3x)(2x - 3y)$ 19. $3y^2 - 5yx^2 + 12y - 20x^2 = y(3y - 5x^2) + 4(3y - 5x^2) = (3y - 5x^2)(y + 4)$ 20. $7x^2 - 20y^2 + 14y^2 - 10x^2 = -3x^2 - 6y^2 = -3(x^2 + 2y^2)$