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.Answer:
I. Worksheet on factorization using formula when a binomial is the difference of two squares:
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. Worksheet on factorization using formula when the given expression is a perfect square:
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
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