Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 992 · 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.If a + b = 15 and ab = 36, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 101 × 99.
3. 3.If a + b = 13 and ab = 12, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 96 × 84.
5. 5.Use (a + b)² = a² + 2ab + b² to find 52².
6. 6.Use a² − b² = (a + b)(a − b) to find 71² − 45².
7. 7.Use (a + b)² = a² + 2ab + b² to find 73².
8. 8.Use a² − b² = (a + b)(a − b) to find 24² − 3².
9. 9.If a + b = 5 and ab = 4, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 26².
11. 11.Use a² − b² = (a + b)(a − b) to find 42² − 20².
12. 12.Use (a + b)(a − b) = a² − b² to find 54 × 46.
13. 13.Use (a + b)² = a² + 2ab + b² to find 103².
14. 14.Use (a + b)² = a² + 2ab + b² to find 56².
15. 15.Use (a + b)(a − b) = a² − b² to find 82 × 78.
16. 16.Use (a − b)² = a² − 2ab + b² to find 53².
17. 17.Use (a − b)² = a² − 2ab + b² to find 54².
18. 18.If a + b = 14 and ab = 40, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 71².
20. 20.Use (a − b)² = a² − 2ab + b² to find 88².
21. 21.If a + b = 19 and ab = 84, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 35².
23. 23.Use (a + b)(a − b) = a² − b² to find 98 × 82.
24. 24.If a + b = 12 and ab = 11, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 27².
26. 26.Use (a − b)² = a² − 2ab + b² to find 55².
27. 27.If a + b = 16 and ab = 48, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 55 × 45.
29. 29.If a − b = 1 and ab = 2, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 74².
31. 31.If a + b = 6 and ab = 5, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 76 × 64.
33. 33.Use (a + b)² = a² + 2ab + b² to find 106².
34. 34.Use (a + b)² = a² + 2ab + b² to find 78².
35. 35.Use (a + b)(a − b) = a² − b² to find 37 × 23.
36. 36.Use (a + b)(a − b) = a² − b² to find 99 × 81.
37. 37.Use (a + b)² = a² + 2ab + b² to find 21².
38. 38.Use (a + b)² = a² + 2ab + b² to find 77².
39. 39.Use (a − b)² = a² − 2ab + b² to find 76².
40. 40.Use (a + b)(a − b) = a² − b² to find 83 × 77.

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