Margföldun – Æfing 3.6 – Lausnir

  1. (16a2 + 9)(4a – 3)(4a + 3) = (16a2 + 9)(16a2 – 9) = 256a2 – 81 (notum samokaregluna tvisvar)
  2. (5x + 1)(25x2 – 1)(5x – 1) = (25x2 – 1)(25x2 + 1) = 625x2 – 1 (notum samokaregluna tvisvar)
  3. (s + 2)(s2 – 4)(s – 2) = (s2 – 4)(s2 – 4) = s4 – 8s2 – 16 (notum samokaregluna einu sinni og síðan ferningsreglu)
  4. (p + 1)2 – (p – 1)2 = p2 + 2p + 1 – (p2 – 2p + 1) = p2 + 2p + 1 – p2 + 2p – 1 = 4p2
  5. 2(x + 3)2 + 2(x – 3)2 = 2(x2 + 6x + 9) + 2(x2 – 6x + 9) = 2x2 + 12x + 18 + 2x2 – 12x + 18 = 4x2 + 36
  6. (p + q)2 + (p + q)(p – q) = p2 +2pq + q2 + p2 – q2 = 2p2 + 2pq = 2p(p + q)
  7. ((3x + 2)(3x – 2))2 = (9x2 – 4)2 = 81x4 – 72x2 + 16