Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 603 · 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 21 × 19.
2. 2.Use (a + b)(a − b) = a² − b² to find 41 × 39.
3. 3.Use (a − b)² = a² − 2ab + b² to find 29².
4. 4.If a + b = 3 and ab = 2, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 61² − 51².
6. 6.Find the value of x² + 2xy + y² when x = 5 and y = 3.
7. 7.If a − b = 1 and ab = 12, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 41².
9. 9.If a + b = 13 and ab = 42, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 61².
11. 11.Use a² − b² = (a + b)(a − b) to find 81² − 60².
12. 12.If a + b = 20 and ab = 96, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 73².
14. 14.Use (a + b)² = a² + 2ab + b² to find 22².
15. 15.Use a² − b² = (a + b)(a − b) to find 32² − 22².
16. 16.Use (a + b)(a − b) = a² − b² to find 63 × 57.
17. 17.If a − b = 10 and ab = 24, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 25² − 17².
19. 19.Use a² − b² = (a + b)(a − b) to find 83² − 64².
20. 20.Use (a + b)(a − b) = a² − b² to find 85 × 75.
21. 21.Find the value of x² − y² when x = 3 and y = 1.
22. 22.Use a² − b² = (a + b)(a − b) to find 20² − 1².
23. 23.Use (a − b)² = a² − 2ab + b² to find 17².
24. 24.Use (a + b)(a − b) = a² − b² to find 61 × 59.
25. 25.Use (a + b)² = a² + 2ab + b² to find 86².
26. 26.Use (a + b)² = a² + 2ab + b² to find 32².
27. 27.Use a² − b² = (a + b)(a − b) to find 39² − 6².
28. 28.Use (a + b)(a − b) = a² − b² to find 95 × 85.
29. 29.Use a² − b² = (a + b)(a − b) to find 58² − 8².
30. 30.Use (a + b)(a − b) = a² − b² to find 98 × 82.
31. 31.Use (a − b)² = a² − 2ab + b² to find 23².
32. 32.Find the value of x² + 2xy + y² when x = 3 and y = 1.
33. 33.Use (a − b)² = a² − 2ab + b² to find 26².
34. 34.Use (a − b)² = a² − 2ab + b² to find 19².
35. 35.Use (a − b)² = a² − 2ab + b² to find 85².
36. 36.Use (a + b)² = a² + 2ab + b² to find 48².
37. 37.Use a² − b² = (a + b)(a − b) to find 54² − 40².
38. 38.Use (a − b)² = a² − 2ab + b² to find 95².
39. 39.Use a² − b² = (a + b)(a − b) to find 84² − 29².
40. 40.Use (a + b)(a − b) = a² − b² to find 29 × 11.

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