Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 701 · 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 46².
2. 2.If a + b = 4 and ab = 3, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 81².
4. 4.If a + b = 7 and ab = 6, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 41 × 39.
6. 6.Use (a + b)² = a² + 2ab + b² to find 53².
7. 7.Use (a − b)² = a² − 2ab + b² to find 65².
8. 8.If a − b = 6 and ab = 55, what is a² + b²?
9. 9.Find the value of x² − y² when x = 13 and y = 9.
10. 10.Use (a + b)(a − b) = a² − b² to find 83 × 77.
11. 11.If a − b = 1 and ab = 12, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 83² − 12².
13. 13.Use a² − b² = (a + b)(a − b) to find 82² − 47².
14. 14.Use (a + b)² = a² + 2ab + b² to find 45².
15. 15.Use (a + b)(a − b) = a² − b² to find 21 × 19.
16. 16.Use (a + b)² = a² + 2ab + b² to find 41².
17. 17.If a + b = 7 and ab = 12, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 105 × 95.
19. 19.Use (a − b)² = a² − 2ab + b² to find 98².
20. 20.Find the value of x² + 2xy + y² when x = 10 and y = 1.
21. 21.Use (a − b)² = a² − 2ab + b² to find 26².
22. 22.Use (a + b)² = a² + 2ab + b² to find 109².
23. 23.Use (a + b)² = a² + 2ab + b² to find 91².
24. 24.Use (a + b)² = a² + 2ab + b² to find 43².
25. 25.Use a² − b² = (a + b)(a − b) to find 29² − 18².
26. 26.Use (a − b)² = a² − 2ab + b² to find 58².
27. 27.Use (a + b)² = a² + 2ab + b² to find 77².
28. 28.Use (a + b)(a − b) = a² − b² to find 71 × 69.
29. 29.Use (a − b)² = a² − 2ab + b² to find 11².
30. 30.If a − b = 1 and ab = 2, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 85² − 58².
32. 32.If a + b = 6 and ab = 8, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 31².
34. 34.Use (a + b)² = a² + 2ab + b² to find 15².
35. 35.Use (a + b)(a − b) = a² − b² to find 96 × 84.
36. 36.Use (a + b)(a − b) = a² − b² to find 108 × 92.
37. 37.Use (a − b)² = a² − 2ab + b² to find 63².
38. 38.Use (a − b)² = a² − 2ab + b² to find 41².
39. 39.If a + b = 9 and ab = 20, what is a² + b²?
40. 40.If a + b = 11 and ab = 30, what is a² + b²?

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