Þáttun – Æfing 4.4 – Lausnir

  1. A10 – B8 = (A5 – B4)(A5 + B4) (samokareglan notuð)
  2. 12x2-75b2 = 3(4x2 – 25b2) = 3(2x – 5b)(2x + 5b) (samokareglan notuð)
  3. 20a2 – 45b2 = 5(4a2 – 9b2) = 5(2a – 3b)(2a + 3b) (samokareglan notuð)
  4. 16y2 + 32y + 16 = 4(4y2 + 8y + 4) = 4(2y + 2)2 (ferningsreglan notuð)
  5. 8z2 – 16z + 8 = 8(z2 – 2z + 1) = 8(z – 1)2 (ferningsreglan notuð)
  6. 12x2 – 36ax +27 = 3(4x2 – 12x + 9) = 3(2x – 3)2 (ferningsreglan notuð)
  7. r2 + 2rs + s2 – t2 = (r + s)2 – t2 = ((r + s) + t)((r + s) – t) = (r + s + t)(r + s – t) (bæði ferningsregla og samokaregla eru notaðar)
  8. p2 – 2pq + q2 – x2 = (p – q)2 – x2 = ((p – q) – x)((p – q) + x) = (p – q – x)(p + q + x) (bæði ferningsregla og samokaregla eru notaðar)
  9. a2 – c2 – 2ab + b2 = a2 – 2ab + b2 – c2 = (a – b)2 – c2 = ((a – b) – c)((a – b) + c) = (a – b – c)(a – b + c)   (bæði ferningsregla og samokaregla eru notaðar)