Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 644 · 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.If a − b = 3 and ab = 4, what is a² + b²?
3. 3.Find the value of x² − y² when x = 14 and y = 7.
4. 4.Use a² − b² = (a + b)(a − b) to find 74² − 40².
5. 5.Find the value of x² − y² when x = 13 and y = 2.
6. 6.Use (a − b)² = a² − 2ab + b² to find 58².
7. 7.Use (a + b)(a − b) = a² − b² to find 102 × 98.
8. 8.Use (a + b)(a − b) = a² − b² to find 96 × 84.
9. 9.Use (a + b)² = a² + 2ab + b² to find 53².
10. 10.Use (a − b)² = a² − 2ab + b² to find 46².
11. 11.If a + b = 5 and ab = 6, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 75².
13. 13.Use (a − b)² = a² − 2ab + b² to find 39².
14. 14.If a + b = 17 and ab = 60, what is a² + b²?
15. 15.If a + b = 15 and ab = 36, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 93².
17. 17.Use (a + b)² = a² + 2ab + b² to find 59².
18. 18.Use (a − b)² = a² − 2ab + b² to find 86².
19. 19.Find the value of x² + 2xy + y² when x = 3 and y = 1.
20. 20.Use (a + b)(a − b) = a² − b² to find 77 × 63.
21. 21.Use (a + b)² = a² + 2ab + b² to find 35².
22. 22.Use a² − b² = (a + b)(a − b) to find 65² − 63².
23. 23.Use (a − b)² = a² − 2ab + b² to find 26².
24. 24.Use a² − b² = (a + b)(a − b) to find 67² − 11².
25. 25.Use (a + b)² = a² + 2ab + b² to find 89².
26. 26.If a + b = 15 and ab = 50, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 21².
28. 28.Find the value of x² + 2xy + y² when x = 4 and y = 1.
29. 29.Use (a + b)² = a² + 2ab + b² to find 68².
30. 30.Find the value of x² − 2xy + y² when x = 7 and y = 1.
31. 31.Use a² − b² = (a + b)(a − b) to find 30² − 7².
32. 32.Use (a − b)² = a² − 2ab + b² to find 45².
33. 33.Use a² − b² = (a + b)(a − b) to find 75² − 48².
34. 34.If a − b = 4 and ab = 45, what is a² + b²?
35. 35.Find the value of x² + 2xy + y² when x = 11 and y = 6.
36. 36.Use a² − b² = (a + b)(a − b) to find 43² − 5².
37. 37.If a − b = 1 and ab = 20, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 52².
39. 39.Use a² − b² = (a + b)(a − b) to find 93² − 4².
40. 40.Use a² − b² = (a + b)(a − b) to find 48² − 17².

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