Номер 722

1) m2n2m + n = (mn)(m + n) – (mn) = (mn)(m + n – 1).

2) c + dc2 + d2 = (c + d) – (cd)(c + d) = (c + d)(1 – (cd)) = (c + 1)(1 – c + d).

3) 16x2 – 25y2 – 4x – 5y = (4x – 5y)(4x + 5y) – (4x + 5y) = (4x + 5y)(4x – 5y – 1).

4) 12a2b3 + 3a3b2 + 16b2a2 = 3a2b2(4b + a) + (4ba)(4b + a) = (4b + a)(3a2b2 + 4ba).

5) 49c2 – 14c + 1 – 21ac + 3a = (7c – 1)2 – 3a(7c – 1) = (7c – 1)(7c – 1 – 3a).

6) ax2 + ay2 + x4 + 2x2y2 + y4 = a(x2 + y2) + (x2 + y2)2 = (x2 + y2)(a + x2 + y2).

7) 27c3d3 + 9c2 + 3cd + d2 = (3cd)(9c2 + 3cd + d2) + (9c2 + 3cd + d2) = (9c2 + 3cd + d2)(3cd + 1).

8) b3 – 2b2 – 2b + 1 = (b3 + 1) – (2b2 + 2b) = (b + 1)(b2b + 1) – 2b(b + 1) = (b + 1)(b2b + 1 – 2b) = (b + 1)(b2 – 3b + 1).


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