Special Products and Expansions

Exercise

  1. Simplify the following:
    (i)
    (ii)
    (iii) (2 +x)(2 -x)
    (iv) (2x +3)(2x +4)
    (v) (3x -1)(3x -2)
    (vi) (3s -4t)²
    (vii) (a² +b²)²
    (viii)
    (ix) (x +y +z)(x +y -z)
    (x)
    (xi) (2 +x)²
    (xii) (2 +3)²
  2. If a -1/a = 3, find
    (i) a² +1/a²
    (ii) a4 +1/a4
  3. If a +1/a = 3, find
    (i) a² +1/a²
    (ii) a4 +1/a4
  4. Simplify the following:
    (i) (a +b)² +(a -b)²
    (ii) (a +b)² -(a -b)²
    (iii)
    (iv)
  5. Use (a +b)² = a² +2ab +b² to evaluate
    (i) (101)²
    (ii) (10.2)²
  6. Use (a -b)² = a² -2ab +b² to evaluate
    (i) (997)²
    (ii) (9.8)²
  7. Evaluate 1002×998 by using a special product.
  8. Fill in the blanks in the following:
    (i) (2x -...)² = 4x² -... +9y²
    (ii) (a +...)² =... +... +4b²
    (iii) (3s +2t)(3s -2t) =... -...
  9. Simplify .
  10. Simplify (x -2)(x +2)(x² +4)(x4 +16).
  11. Simplify
  12. If x -1/x = 5, find the value of x² +1/x²

Answers

1. (i) 4a² -b²/4  (ii) x² -1/4   (iii) 4 -x²
    (iv) 4x² +14x +12             (v) 9x² -9x +2
    (vi) 9s² -24st +16t²          (vii) a4 +2a²b² +b4
    (viii) 9a4 -2 +1/9a4               (ix) x² +2xy +y² -z² (x) x²/2 +8/y² +4x/y
    (xi) 2 +2 2x +x2                (xii) 5 +26.
2. (i) 11      (ii) 119      3. (i)7               (ii) 47
4. (i) 2 (a² +b²)             (ii) 4ab             (iii)
(iv) 4                          5. (i) 10201      (ii) 104.04.
6. (i) 994009               (ii) 96.04          7. 999996
8. (i) 3y, 12xy               (ii) 2b,a², 4ab  (iii) 9s² , 4t²
9. 1/2 x² -2                10. x8 -256
11. x² +1/x²+3 -2x -2/x   12. 7