Номер 721

Розкладіть на множники:

1) a2b2ab = (ab)(a + b) – (a + b) = (a + b)(ab – 1).

2) x – yx2 + y2 = (xy) – (x2y2) = (xy) – (xy)(x + y) = (xy)(1 – xy).

3) 4m2 – 9n2 + 2m + 3n = (2m – 3n)(2m + 3n) + (2m + 3n) = (2m + 3n)(2m – 3n + 1).

4) c2d2 + 4c – 4d = (cd)(c + d) + 4(cd) = (cd)(c + d + 4).

5) 5x2y – 5xy2x2 + y2 = 5xy(xy) – (xy)(x + y) = (xy)(5xy – (x + y)) = (xy)(5xyxy).

6) a2 – 10a + 25 – ab + 5b = (a – 5)2b(a – 5) = (a – 5)(a – 5 – b).

7) 8mp + 8npm2 – 2mnn2 = 8p(m + n) – (m + n)2 = (m + n)(8pmn).

8) a3 + b3a2bab2 = (a + b)(a2ab + b2) – ab(a + b) = (a + b)(a2ab + b2ab) = (a + b)(ab)2.

9) m3 – 8n3m2 + 4mn – 4n2 = (m – 2n)(m2 + 2mn + 4n2) – (m2 – 4mn + 4n2) =
= (m – 2n)(m2 + 2mn + 4n2) – (m – 2n)2 = (m – 2n)(m2 + 2mn + 4n2m + 2n).

10) a3 – 4a2 + 4a – 1 = (a3 – 1) – (4a2 – 4a) = (a – 1)(a2 + a + 1) – 4a(a – 1) = (a – 1)(a2 + a + 1 – 4a) = (a – 1)(a2 – 3a + 1).


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