Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 652 · 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 61 × 59.
2. 2.Find the value of x² − y² when x = 12 and y = 2.
3. 3.Use (a − b)² = a² − 2ab + b² to find 88².
4. 4.If a − b = 7 and ab = 8, what is a² + b²?
5. 5.If a − b = 3 and ab = 10, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 54².
7. 7.Find the value of x² + 2xy + y² when x = 4 and y = 1.
8. 8.Find the value of x² − 2xy + y² when x = 7 and y = 3.
9. 9.If a + b = 3 and ab = 2, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 86².
11. 11.If a + b = 12 and ab = 35, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 108 × 92.
13. 13.Use (a + b)² = a² + 2ab + b² to find 93².
14. 14.Use (a + b)(a − b) = a² − b² to find 95 × 85.
15. 15.Use a² − b² = (a + b)(a − b) to find 90² − 53².
16. 16.Use (a + b)(a − b) = a² − b² to find 47 × 33.
17. 17.Use (a + b)(a − b) = a² − b² to find 76 × 64.
18. 18.Find the value of x² − y² when x = 10 and y = 5.
19. 19.Use (a + b)² = a² + 2ab + b² to find 14².
20. 20.Use (a + b)(a − b) = a² − b² to find 104 × 96.
21. 21.Use (a − b)² = a² − 2ab + b² to find 48².
22. 22.Use (a + b)² = a² + 2ab + b² to find 15².
23. 23.Use (a + b)² = a² + 2ab + b² to find 41².
24. 24.Use (a + b)² = a² + 2ab + b² to find 52².
25. 25.Use a² − b² = (a + b)(a − b) to find 31² − 5².
26. 26.If a − b = 5 and ab = 36, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 19².
28. 28.Use (a + b)² = a² + 2ab + b² to find 73².
29. 29.If a + b = 20 and ab = 99, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 26² − 6².
31. 31.If a − b = 3 and ab = 28, what is a² + b²?
32. 32.Find the value of x² − 2xy + y² when x = 10 and y = 1.
33. 33.Use (a + b)(a − b) = a² − b² to find 33 × 27.
34. 34.Use (a + b)² = a² + 2ab + b² to find 106².
35. 35.If a + b = 18 and ab = 80, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 93 × 87.
37. 37.Use (a − b)² = a² − 2ab + b² to find 28².
38. 38.Find the value of x² − 2xy + y² when x = 6 and y = 5.
39. 39.Use a² − b² = (a + b)(a − b) to find 89² − 82².
40. 40.If a − b = 1 and ab = 2, what is a² + b²?

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