Розділ 2. РОЗКЛАДАННЯ МНОГОЧЛЕНІВ » 641

Розклади на множники многочлен. a) (3a + 2p)2 – (a + p)2 = (3a + 2p – (a + p))(3a + 2p + a + p) = (3a+ + 2p – a – p)(4a + 3p) = (2a + p)(4a + 3p); б) 9(p + q)2 – (p – q)2 = (3(p + q) – (p – q))(3(p + q) + p – q) = (3p + 3q – p + q)(3p + 3q + p – q) = (2p + 4q)(4p + 2q); в) a4 – 2a2 + 1 – p2 + 2pc – c2 = (a2 – 1)2 – (p2 – 2pc + c2) = (a2 – 1)2 – (p – c)2 = (a2 – 1 – (p – c))(a2 – 1 + p – c) = (a2 – 1 – p + c)(a2 – 1 + p – c); г) p2 + 6pq + 9q2 – a2 + 4a – 4 = (p + 3q)2 – (a2 – 4a + 4) = (p + 3q)2 – (a – 2)2 = (p + 3q – (a – 2))(p + 3q + a – 2) = (p + 3q – a + 2)(p + 3q + a – 2).