Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 881 · 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 76² − 40².
2. 2.Use a² − b² = (a + b)(a − b) to find 99² − 86².
3. 3.Use (a − b)² = a² − 2ab + b² to find 45².
4. 4.Use (a + b)² = a² + 2ab + b² to find 87².
5. 5.If a − b = 3 and ab = 4, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 81² − 51².
7. 7.If a − b = 5 and ab = 66, what is a² + b²?
8. 8.Find the value of x² + 2xy + y² when x = 14 and y = 7.
9. 9.Use a² − b² = (a + b)(a − b) to find 43² − 20².
10. 10.Use a² − b² = (a + b)(a − b) to find 71² − 9².
11. 11.Use a² − b² = (a + b)(a − b) to find 63² − 13².
12. 12.Use (a + b)(a − b) = a² − b² to find 101 × 99.
13. 13.Use a² − b² = (a + b)(a − b) to find 74² − 11².
14. 14.Use (a + b)(a − b) = a² − b² to find 36 × 24.
15. 15.Use a² − b² = (a + b)(a − b) to find 55² − 2².
16. 16.Use (a + b)² = a² + 2ab + b² to find 75².
17. 17.Use (a + b)² = a² + 2ab + b² to find 24².
18. 18.Use a² − b² = (a + b)(a − b) to find 46² − 23².
19. 19.Use (a + b)(a − b) = a² − b² to find 97 × 83.
20. 20.If a + b = 5 and ab = 6, what is a² + b²?
21. 21.Find the value of x² − 2xy + y² when x = 9 and y = 7.
22. 22.Use (a + b)(a − b) = a² − b² to find 86 × 74.
23. 23.Use (a + b)² = a² + 2ab + b² to find 72².
24. 24.Use (a + b)(a − b) = a² − b² to find 73 × 67.
25. 25.Use (a + b)(a − b) = a² − b² to find 76 × 64.
26. 26.Use a² − b² = (a + b)(a − b) to find 71² − 54².
27. 27.If a − b = 3 and ab = 18, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 77².
29. 29.Use (a + b)² = a² + 2ab + b² to find 22².
30. 30.If a − b = 1 and ab = 56, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 53².
32. 32.If a − b = 1 and ab = 90, what is a² + b²?
33. 33.Find the value of x² − 2xy + y² when x = 10 and y = 1.
34. 34.Use (a + b)(a − b) = a² − b² to find 48 × 32.
35. 35.Use a² − b² = (a + b)(a − b) to find 83² − 52².
36. 36.Use (a + b)² = a² + 2ab + b² to find 39².
37. 37.Use (a + b)² = a² + 2ab + b² to find 15².
38. 38.Use a² − b² = (a + b)(a − b) to find 70² − 46².
39. 39.Use (a + b)² = a² + 2ab + b² to find 63².
40. 40.Use (a + b)² = a² + 2ab + b² to find 108².

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