Вправи: 83

83. Спростіть вираз:

1) 16-7a(3-a)2 – 13-6a(a-3)2 = 16-7a(3-a)2 – 13-6a(3-a)2 = 16-7a-(13-6a)(3-a)2 = 16-7a-13+6a(3-a)2 = 3-a(3-a)2 = 13-a;

2) 15(2m -3)(3-m)3 + 5m2(m-3)3 = 5m2(m-3)3 – 15(2m-3)(m-3)3 = 5m2- 30m+45(m-3)3 = 5(m2- 6m+9)(m-3)3 = 5(m-3)2(m-3)3 = 5m-3;

3) p2- 9qp-3(q-4) – 3(p-3q)3-p(4-q).

Оскільки (3 – p)(4 – q) = (–(p – 3)) • (–(q – 4)) = (p – 3)(q – 4), то маємо p2- 9qp-3(q-4) – 3(p-3q)3-p(4-q) = p2- 9q-3p+9qp-3(q-4) = p2- 3pp-3(q-4) = p(p-3)p-3(q-4) = pq-4.