Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 692 · 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 (a + b)² = a² + 2ab + b² to find 105².
2. 2.If a + b = 5 and ab = 6, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 69².
4. 4.If a − b = 4 and ab = 5, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 14².
6. 6.Use (a − b)² = a² − 2ab + b² to find 67².
7. 7.If a − b = 2 and ab = 3, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 77 × 63.
9. 9.Use a² − b² = (a + b)(a − b) to find 72² − 62².
10. 10.Use a² − b² = (a + b)(a − b) to find 34² − 14².
11. 11.Find the value of x² + 2xy + y² when x = 11 and y = 9.
12. 12.Use a² − b² = (a + b)(a − b) to find 83² − 18².
13. 13.Use (a + b)(a − b) = a² − b² to find 101 × 99.
14. 14.Use (a + b)(a − b) = a² − b² to find 22 × 18.
15. 15.If a − b = 2 and ab = 15, what is a² + b²?
16. 16.Find the value of x² − 2xy + y² when x = 7 and y = 2.
17. 17.If a + b = 18 and ab = 77, what is a² + b²?
18. 18.Find the value of x² − 2xy + y² when x = 15 and y = 14.
19. 19.Use (a + b)² = a² + 2ab + b² to find 22².
20. 20.Use a² − b² = (a + b)(a − b) to find 72² − 25².
21. 21.Use (a − b)² = a² − 2ab + b² to find 21².
22. 22.If a − b = 7 and ab = 44, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 53².
24. 24.Use a² − b² = (a + b)(a − b) to find 42² − 28².
25. 25.Use (a + b)(a − b) = a² − b² to find 105 × 95.
26. 26.If a + b = 3 and ab = 2, what is a² + b²?
27. 27.If a − b = 1 and ab = 2, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 61².
29. 29.Use (a − b)² = a² − 2ab + b² to find 13².
30. 30.If a − b = 1 and ab = 30, what is a² + b²?
31. 31.If a − b = 4 and ab = 21, what is a² + b²?
32. 32.If a + b = 15 and ab = 54, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 85².
34. 34.Use (a + b)(a − b) = a² − b² to find 86 × 74.
35. 35.Use (a + b)(a − b) = a² − b² to find 61 × 59.
36. 36.If a + b = 9 and ab = 8, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 36² − 22².
38. 38.Use (a − b)² = a² − 2ab + b² to find 82².
39. 39.Use a² − b² = (a + b)(a − b) to find 58² − 18².
40. 40.Use a² − b² = (a + b)(a − b) to find 25² − 24².

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