Вправи: 508

508. Розкладіть на множники вираз:

1) (5 + b)² – b² = (5 + b – b)(5 + b + b) = 5(5 + 2b);

2) (4 – b)² – 16 = (4 – b)² – 4² = (4 – b – 4)(4 – b + 4) = –b(8 – b);

3) у² – (7 + у)² = (y + 7 + y)(y – 7 – y) = –7(2y + 7);

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

5) (1 + х)² – (1 – х)² = (1 + x + 1 – x)(1 + x – 1 + x) = 4x;

6) (х + 2)² – (2 + х)² = (x + 2 + 2 + x)(x + 2 – 2 – x) = (2x + 4) • 0 = 0;

7) (х + 6)² – (6 – х)² = (x + 6 + 6 – x)(x + 6 – 6 + x) = 24x;

8) (Зx + 2)² – (5 – х)² = (3x + 2 + 5 – x)(3x + 2 – 5 + x) = (2x + 7)(4x – 3).