Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 267 · 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)(a − b) = a² − b² to find 31 × 29.
2. 2.Find the value of x² − y² when x = 5 and y = 4.
3. 3.Use a² − b² = (a + b)(a − b) to find 81² − 47².
4. 4.Use a² − b² = (a + b)(a − b) to find 59² − 13².
5. 5.Use a² − b² = (a + b)(a − b) to find 21² − 4².
6. 6.Use (a − b)² = a² − 2ab + b² to find 75².
7. 7.If a + b = 7 and ab = 10, what is a² + b²?
8. 8.If a + b = 21 and ab = 110, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 77².
10. 10.Use (a − b)² = a² − 2ab + b² to find 34².
11. 11.Use (a + b)(a − b) = a² − b² to find 101 × 99.
12. 12.Use (a + b)² = a² + 2ab + b² to find 18².
13. 13.If a + b = 12 and ab = 11, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 29².
15. 15.If a − b = 2 and ab = 15, what is a² + b²?
16. 16.If a + b = 12 and ab = 27, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 66² − 12².
18. 18.Find the value of x² − 2xy + y² when x = 15 and y = 1.
19. 19.Use (a − b)² = a² − 2ab + b² to find 62².
20. 20.Use (a + b)² = a² + 2ab + b² to find 95².
21. 21.Use (a + b)² = a² + 2ab + b² to find 23².
22. 22.Use (a + b)(a − b) = a² − b² to find 27 × 13.
23. 23.If a − b = 5 and ab = 36, what is a² + b²?
24. 24.Find the value of x² − y² when x = 6 and y = 5.
25. 25.Find the value of x² + 2xy + y² when x = 3 and y = 1.
26. 26.Use a² − b² = (a + b)(a − b) to find 21² − 7².
27. 27.Use (a + b)(a − b) = a² − b² to find 62 × 58.
28. 28.Use a² − b² = (a + b)(a − b) to find 78² − 32².
29. 29.Use (a − b)² = a² − 2ab + b² to find 76².
30. 30.Use (a + b)² = a² + 2ab + b² to find 71².
31. 31.Use (a − b)² = a² − 2ab + b² to find 82².
32. 32.Use a² − b² = (a + b)(a − b) to find 20² − 18².
33. 33.Use (a − b)² = a² − 2ab + b² to find 61².
34. 34.Use (a − b)² = a² − 2ab + b² to find 72².
35. 35.Use (a + b)² = a² + 2ab + b² to find 39².
36. 36.If a + b = 3 and ab = 2, what is a² + b²?
37. 37.Find the value of x² − y² when x = 8 and y = 2.
38. 38.Use a² − b² = (a + b)(a − b) to find 94² − 86².
39. 39.Use (a − b)² = a² − 2ab + b² to find 79².
40. 40.Use (a + b)(a − b) = a² − b² to find 57 × 43.

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