№ 49. Разложите на множители многочлен: а) na + nb + 5a + 5b; б) 7x-7y+bx-by; в) 10a-by+10b-ay; г) pq-x-px+q; д) b-a-ab + 1; е) 2cx-cy - 6x + 3у; ж) 15ах-14by+10bx-21ay; з) 56pq-1-7q+8p.

Решение:

1. а) \( na + nb + 5a + 5b = n(a+b) + 5(a+b) = (a+b)(n+5) \)
2. б) \( 7x - 7y + bx - by = 7(x-y) + b(x-y) = (x-y)(7+b) \)
3. в) \( 10a - by + 10b - ay = 10(a+b) - y(b+a) = (a+b)(10-y) \)
4. г) \( pq - x - px + q = pq + q - px - x = q(p+1) - x(p+1) = (p+1)(q-x) \)
5. д) \( b - a - ab + 1 = (b+1) - a(b+1) = (b+1)(1-a) \)
6. е) \( 2cx - cy - 6x + 3y = c(2x-y) - 3(2x-y) = (2x-y)(c-3) \)
7. ж) \( 15ax - 14by + 10bx - 21ay = 15ax + 10bx - 21ay - 14by = 5x(3a+2b) - 7y(3a+2b) = (3a+2b)(5x-7y) \)
8. з) \( 56pq - 1 - 7q + 8p = 56pq + 8p - 7q - 1 = 8p(7q+1) - (7q+1) = (7q+1)(8p-1) \)