Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 753 · 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 86².
2. 2.Use (a + b)(a − b) = a² − b² to find 81 × 79.
3. 3.Use (a − b)² = a² − 2ab + b² to find 58².
4. 4.Find the value of x² + 2xy + y² when x = 13 and y = 12.
5. 5.Use (a + b)(a − b) = a² − b² to find 48 × 32.
6. 6.Use (a + b)(a − b) = a² − b² to find 108 × 92.
7. 7.Use (a − b)² = a² − 2ab + b² to find 97².
8. 8.If a − b = 4 and ab = 5, what is a² + b²?
9. 9.If a − b = 3 and ab = 54, what is a² + b²?
10. 10.If a − b = 5 and ab = 6, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 33 × 27.
12. 12.Use (a + b)² = a² + 2ab + b² to find 72².
13. 13.Use (a + b)² = a² + 2ab + b² to find 103².
14. 14.If a + b = 19 and ab = 84, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 19².
16. 16.Find the value of x² − y² when x = 6 and y = 4.
17. 17.Use a² − b² = (a + b)(a − b) to find 92² − 80².
18. 18.Use (a + b)² = a² + 2ab + b² to find 24².
19. 19.Use a² − b² = (a + b)(a − b) to find 88² − 67².
20. 20.Use (a + b)² = a² + 2ab + b² to find 109².
21. 21.Use (a − b)² = a² − 2ab + b² to find 22².
22. 22.Use (a + b)² = a² + 2ab + b² to find 47².
23. 23.Use a² − b² = (a + b)(a − b) to find 84² − 6².
24. 24.Use (a + b)(a − b) = a² − b² to find 103 × 97.
25. 25.Find the value of x² + 2xy + y² when x = 15 and y = 4.
26. 26.Use (a + b)(a − b) = a² − b² to find 25 × 15.
27. 27.If a − b = 2 and ab = 3, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 58² − 29².
29. 29.Use (a − b)² = a² − 2ab + b² to find 67².
30. 30.Use (a − b)² = a² − 2ab + b² to find 33².
31. 31.Use (a − b)² = a² − 2ab + b² to find 87².
32. 32.If a + b = 5 and ab = 6, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 25².
34. 34.If a − b = 4 and ab = 12, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 61² − 53².
36. 36.Use (a − b)² = a² − 2ab + b² to find 81².
37. 37.Use (a − b)² = a² − 2ab + b² to find 74².
38. 38.Use a² − b² = (a + b)(a − b) to find 38² − 9².
39. 39.Use (a − b)² = a² − 2ab + b² to find 26².
40. 40.Use (a + b)(a − b) = a² − b² to find 58 × 42.

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