Exercises 3 (Factorising)

Multiply out of following brackets and show that:

  1. \((x+2)(x+4) = x^2 + 6x + 8\)

  2. \((-x-7)(2-3x)=3x^2+19x-14\)

  3. \((7t+6)(5t+8)=35t^2+86t+48\)

  4. \((s-5)(s+6) = s^2+s-30\)

  5. \((2q+3)(3q-5)=6q^2-q-15\)

  6. \((x-4)(3x-1) = 3x^2-13x +4\)

  7. \((x-2)(x+2)=x^2-4\)

  8. \((2x-1)(2x-1) = 4x^2-4x+1\)

  9. \((x+4)^2 = x^2 + 8x + 16\)

  10. \((3x+5)^2=9x^2+30x+25\)

Factorise the following quadratic polynomials:

  1. \(x^2+8x+15\)

  2. \(x^2+11x+28\)

  3. \(x^2+7x+6\)

  4. \(x^2-10x+9\)

  5. \(x^2-6x+9\)

  6. \(x^2+5x-14\)

  7. \(x^2-4x-5\)

  8. \(x^2-10x-24\)

  9. \(x^2-1\)

  10. \(x^2-16\)

  11. \(4+5x+x^2\)

  12. \(2x^2-3x+1\)

  13. \(9x^2-6x+1\)

  14. \(9+6x+x^2\)

  15. \(x^2+2ax+a^2\)

  16. \(4x^2-9\)

  17. \(6x^2+x-12\)

  18. \(4x^2-11x+6\)

  19. \(4x^2+3x-1\)

  20. \(3x^2 - 17x+10\)

  21. \(25x^2-16\)

  22. \(3-2x-x^2\)

  23. \(x^2+2xy+y^2\)

  24. \(9-4x^2\)

  25. \(x^2-y^2\)

  26. \(81x^2-36xy+4y^2\)

  27. \(49-84x+36x^2\)

  28. \(36x^2+60xy+25y^2\)

  29. \(4x^2-4xy-3y^2\)

  30. \(49p^2q^2 - 28pq +4\)

Solutions: 11. \((x+3)(x+5)\) 12. \((x+7)(x+4)\) 13. \((x+6)(x+1)\) 14. \((x-9)(x-1)\) 15. \((x-3)(x-3)\) 16. \((x+7)(x-2)\) 17. \((x-5)(x+1)\) 18. \((x-12)(x+2)\) 19. \((x+1)(x-1)\) 20. \((x+4)(x-4)\) 21. \((x+1)(x+4)\) 22. \((2x-1)(x-1)\) 23. \((3x-1)(3x-1)\) 24. \((x+3)(x+3)\) 25. \((x+a)(x+a)\) 26. \((2x+3)(2x-3)\) 27. \((2x+3)(3x-4)\) 28. \((x-2)(4x-3)\) 29. \((4x-1)(x+1)\) 30. \((3x-2)(x-5)\) 31. \((5x-4)(5x+4)\) 32. \((3+x)(1-x)\) 33. \((x+y)(x+y)\) 34. \((3-2x)(3+2x)\) 35. \((x-y)(x+y)\) 36. \((9x-2y)(9x-2y)\) 37. \((7-6x)(7-6x)\) 38. \((6x+5y)(6x+5y)\) 39. \((2x-3y)(2x+y)\) 40. \((7pq-2)(7pq-2)\)