Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 562 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.Use a² − b² = (a + b)(a − b) to find 70² − 67².
2. 2.Use (a + b)(a − b) = a² − b² to find 34 × 26.
3. 3.Use a² − b² = (a + b)(a − b) to find 98² − 14².
4. 4.Find the value of x² + 2xy + y² when x = 10 and y = 5.
5. 5.Use (a + b)² = a² + 2ab + b² to find 12².
6. 6.If a − b = 2 and ab = 3, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 37² − 6².
8. 8.If a − b = 1 and ab = 132, what is a² + b²?
9. 9.If a − b = 7 and ab = 44, what is a² + b²?
10. 10.If a + b = 13 and ab = 30, what is a² + b²?
11. 11.If a + b = 10 and ab = 9, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 63².
13. 13.Use (a + b)(a − b) = a² − b² to find 25 × 15.
14. 14.Find the value of x² − y² when x = 5 and y = 3.
15. 15.Use (a − b)² = a² − 2ab + b² to find 76².
16. 16.If a + b = 5 and ab = 6, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 25².
18. 18.Use (a − b)² = a² − 2ab + b² to find 22².
19. 19.If a + b = 8 and ab = 7, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 76².
21. 21.Use (a − b)² = a² − 2ab + b² to find 78².
22. 22.Use (a − b)² = a² − 2ab + b² to find 51².
23. 23.If a + b = 5 and ab = 4, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 49 × 31.
25. 25.If a − b = 1 and ab = 2, what is a² + b²?
26. 26.Find the value of x² + 2xy + y² when x = 14 and y = 5.
27. 27.Use (a − b)² = a² − 2ab + b² to find 21².
28. 28.Use (a + b)² = a² + 2ab + b² to find 99².
29. 29.Use (a + b)² = a² + 2ab + b² to find 28².
30. 30.Use a² − b² = (a + b)(a − b) to find 32² − 27².
31. 31.Find the value of x² − y² when x = 14 and y = 13.
32. 32.If a − b = 4 and ab = 60, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 61².
34. 34.Use (a + b)² = a² + 2ab + b² to find 62².
35. 35.Use (a − b)² = a² − 2ab + b² to find 19².
36. 36.Use a² − b² = (a + b)(a − b) to find 58² − 16².
37. 37.Use (a + b)² = a² + 2ab + b² to find 45².
38. 38.Use (a + b)² = a² + 2ab + b² to find 65².
39. 39.Find the value of x² + 2xy + y² when x = 6 and y = 5.
40. 40.Use (a − b)² = a² − 2ab + b² to find 46².

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