Вправи: 1355

1355. Розклади на множники многочлен.

а) а² – b² – а + b = (a – b)(a + b) – (а – b) = (a – b)(a + b – 1);

б) x + y + x² – y² = (x + y) + (x – y)(x + y) = (x + y)(1 + x – y);

в) 4а² – 9 – 2а – 3 = (2a – 3)(2a + 3) – (2a + 3) = (2a + 3)(2a – 3 – 1) = (2a + 3)(2а – 4);

г) 5 – 3х + 25 – 9x² = (5 – 3х) + (5 – 3х)(5 + 3х) = (5 – 3х)(1 + 5 + 3х) = (5 – 3х)(6 + 3х) = 3(5 – 3x)(2 + x).