Worksheet on Factorization using Formula

In worksheet on factorization using formula we will solve numerous questions on factorization when a binomial is the difference of two squares and also on factorization when the given expression is a perfect square.

I. Worksheet on factorization using formula when a binomial is the difference of two squares:

1. x2 - 36

2. 4a2 - 9

3. 81 - 49x2

4. 4x2 - 9y2

5. 16x2 - 225y2

6. 9x2y2 25

7. 16x2 - 1/144

8. (2a + 3b)2 - 16c2

9. 1 - (b - c)2

10. 9(x + y)2 - x2

11. 25(a + b)2 - 16(a - b)2

12. 20a2 - 45b2

13. x3 - 64x

14. 12x2 - 27

15. 3x5 - 48x3

16. 63a2b2 - 7

17. a2 - 2ab + b2 - c2

18. x2 - y2 - 2y - 1

19. 9x2 - y2 + 4y - 4

20. x2 - 2xy + y2 - z2

21. 25 - a2 - b2 -2ab

22. 16y3 - 4y

23. 3x5 - 48x

24. (3x - 4y)2 - 25z2

25. (2x + 3y)2 - 1

26. 16c2 - (5a + b)2

27. 100 - (x - 5)2

28. Evaluate:

(i) (405)2 - (395)2

(ii) (7.8)2 - (2.2)2

II. Worksheet on factorization using formula when the given expression is a perfect square:

1. x2 + 8x + 16

2. x2 + 14x + 49

3. 1 + 2x + x2

4. 9 + 6z + z2

5. x2 + 6ax + 9a2

6. 4x2 + 20x +25

7. 36x2 + 36x + 9

8. 9x2 + 24x + 16

9. x2 + x + 1/4

10. x2 - 6x + 9

11. x2 - 10x + 25

12. 9x2 - 12x + 4

13. 16x2 - 24x + 9

14. 1 - 2x + x2

15. 1 - 6x + 9x2

16. a2b2 - 6abc + 9c2

17. m2 - 4mn + 4n2



Answers for this worksheet are given below to check the exact answer.

I. 1. (x + 6)(x - 6)

2. (2a + 3)(2a - 3)

3. (9 + 7x)(9 - 7x)

4. (2x + 3y)(2x - 3y)

5. (4x + 15y)(4x - 15y)

6. (3xy + 5)(3xy - 5)

7. (4x + 1/12)(4x - 1/12)

8. (2a + 3b + 4c)(2a + 3b - 4c)

9. (1 + b - c)(1 - b + c)

10. (4x + 3y)(2x + 3y)

11. (9a + b)(a + 9b)

12. 5(2a + 3b)(2a - 3b)

13. x(x + 8)(x - 8)

14 . 3(2x + 3) (2x - 3)

15. 3x3(x + 4) (x - 4)

16. 7(3ab + 1) (3ab - 1)

17. (a - b + c)(a - b - c)

18. (x + y + 1)(x - y - 1)

19. (3x + y - 2)(3x - y + 2)

20. (x - y + z)(x - y - z)

21. (5 + a + b)(5 - a - b)

22. 4y(2y + 1)(2y - 1)

23. 3x(x2 + 4)(x + 2)(x - 2)

24. (3x - 4y + 5z)(3x - 4y - 5z)

25. (2x + 3y + 1)(2x + 3y - 1)

26. (4c + 5a + b)(4c - 5a - b)

27. (5 + x)(15 - x)

28. (i) 8000 (ii) 56

II. 1. (x + 4)2

2. (x + 7)2

3. (1 + x)2

4. (3 + z)2

5. (x + 3a)2

6. (2x + 5)2

7. (6x + 3)2

8. (3x + 4)2

9. {x + (1/2)}2

10. (x - 3)2

11. (x - 5)2

12. (3x - 2)2

13. (4x - 3)2

14. (1 - x)2

15. (1 - 3x)2

16. (ab - 3c)2

17. (m - 2n)2