Вправи: 632

632. Розклади на множники многочлен.

a) 2ax – axy + 2ay – ay² = a(2x – xy + 2y – y²) = a(x(2 – y) + y(2 – y)) = a(2 – y)(x + y);

б) nx + cx + c³x + c²nx = x(n + c + c²n + c³) = x(n + c + c²(n + c)) = x(n + c)(1 + c²);

в) a³ – ab² – a² – ab = a(a² – b² – a – b) = a((a – b)(a + b) – (a + b)) = a(a + b)(a – b – 1);

г) x² – 2xy + y² + x – y = (x – y)² + (x – y) = (x – y)(x – y + 1).