Вправи: 735

735. Розкладіть на множники многочлен:

1) x² – 4x + 3 = (x² – 4x + 4) – 1 = (x – 2)² – 1 = (x – 2 – 1)(x –2 + 1) = (x – 3)(x – 1);

2) a² + 2a – 24 = (a² + 2a + 1) – 25 = (a + 1)² – 25 = (a + 1 – 5)(a +

+ 1 + 5) = (a – 4)(a + 6);

3) y² + 12y + 35 = (y² + 12y + 36) – 1 = (y + 6)² – 1 = (y + 6 – 1)(y + 6 + 1) = (y + 5)(y + 7);

4) x² + x – 6 (x² + x + 0,25) – 6,25 = (x + 0,5)² – 6,25 = (x + 0,5 –

– 2,5)(x + 0,5 + 2,5) = (x – 2)(x + 3);

5) c² + 8cd + 15d² = (c² + 8cd + 16d²) – d² = (c + 4d)² – d² = (c + 4d + d) = (c + 3d)(c + 5d);

6) 9x² – 30xy + 16y² = (9x² – 30xy + 25y²) – 9y² = (3x – 5y)² – 9y² =

= (3x – 5y – 3y)(3x – 5y + 3y) = (3x – 8y)(3x – 2y).