Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 674 · 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 105².
2. 2.Use (a + b)² = a² + 2ab + b² to find 39².
3. 3.If a + b = 16 and ab = 48, what is a² + b²?
4. 4.If a − b = 4 and ab = 32, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 85².
6. 6.Use (a − b)² = a² − 2ab + b² to find 39².
7. 7.If a − b = 6 and ab = 7, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 103 × 97.
9. 9.Use (a + b)(a − b) = a² − b² to find 47 × 33.
10. 10.Use (a − b)² = a² − 2ab + b² to find 26².
11. 11.Use a² − b² = (a + b)(a − b) to find 28² − 25².
12. 12.If a − b = 3 and ab = 28, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 29².
14. 14.Use a² − b² = (a + b)(a − b) to find 74² − 27².
15. 15.Use (a − b)² = a² − 2ab + b² to find 18².
16. 16.If a + b = 5 and ab = 6, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 48 × 32.
18. 18.Use (a + b)(a − b) = a² − b² to find 76 × 64.
19. 19.Use (a − b)² = a² − 2ab + b² to find 93².
20. 20.Use (a + b)² = a² + 2ab + b² to find 21².
21. 21.Use a² − b² = (a + b)(a − b) to find 58² − 12².
22. 22.Use a² − b² = (a + b)(a − b) to find 20² − 13².
23. 23.Use a² − b² = (a + b)(a − b) to find 52² − 19².
24. 24.Find the value of x² − y² when x = 3 and y = 2.
25. 25.Use (a − b)² = a² − 2ab + b² to find 37².
26. 26.Use (a + b)² = a² + 2ab + b² to find 42².
27. 27.Use (a + b)(a − b) = a² − b² to find 53 × 47.
28. 28.Find the value of x² + 2xy + y² when x = 5 and y = 4.
29. 29.Use (a − b)² = a² − 2ab + b² to find 52².
30. 30.Use (a + b)² = a² + 2ab + b² to find 46².
31. 31.If a − b = 5 and ab = 84, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 77² − 6².
33. 33.Use (a − b)² = a² − 2ab + b² to find 75².
34. 34.Use (a + b)(a − b) = a² − b² to find 38 × 22.
35. 35.Use a² − b² = (a + b)(a − b) to find 83² − 11².
36. 36.Use (a − b)² = a² − 2ab + b² to find 35².
37. 37.If a + b = 7 and ab = 12, what is a² + b²?
38. 38.Find the value of x² − y² when x = 10 and y = 8.
39. 39.Use (a + b)(a − b) = a² − b² to find 91 × 89.
40. 40.If a + b = 13 and ab = 12, what is a² + b²?

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