Вправи: 82

82. Подайте вираз у вигляді дробу:

1) 7-4m(2-m)2 – 9-5m(m-2)2 = 7-4m(m-2)2 – 9-5m(m-2)2 = 7-4m-(9-5m)(m-2)2 = 7-4m-9+5m)(m-2)2 = m-2(m-2)2 = 1m-2;

2) 12a(2-a)3 + 3a2+ 12(a-2)3 = 3a2+ 12(a-2)3 – 12a(a-2)3 = 3a2- 12a+12(a-2)3 = 3(a2- 4a+4)(a-2)3 = 3(a-2)2(a-2)3 = 3a-2;

3) m2- 6nm-2(n-3) – 2(m-3n)2-m(3-n).

Оскільки (2 – m)(3 – n) = (–(m – 2)) • (–(n – 3)) = (m – 2)(n – 3), то маємо m2- 6nm-2(n-3) – 2(m-3n)m-2(n-3) = m2- 6n-2m+6nm-2(n-3) = m2- 2mm-2(n-3) = m(m- 2)m-2(n-3) = mn-3.