Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 964 · 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 44 × 36.
2. 2.Use (a + b)² = a² + 2ab + b² to find 89².
3. 3.Use (a + b)² = a² + 2ab + b² to find 22².
4. 4.Find the value of x² − y² when x = 7 and y = 3.
5. 5.Use (a + b)² = a² + 2ab + b² to find 109².
6. 6.Use a² − b² = (a + b)(a − b) to find 36² − 8².
7. 7.Use (a + b)(a − b) = a² − b² to find 92 × 88.
8. 8.Use (a + b)(a − b) = a² − b² to find 109 × 91.
9. 9.If a − b = 1 and ab = 2, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 81 × 79.
11. 11.Use a² − b² = (a + b)(a − b) to find 56² − 26².
12. 12.Use (a + b)² = a² + 2ab + b² to find 39².
13. 13.Use (a + b)(a − b) = a² − b² to find 67 × 53.
14. 14.Use (a + b)² = a² + 2ab + b² to find 53².
15. 15.Use (a + b)(a − b) = a² − b² to find 43 × 37.
16. 16.If a + b = 18 and ab = 80, what is a² + b²?
17. 17.Find the value of x² − 2xy + y² when x = 6 and y = 5.
18. 18.Use (a − b)² = a² − 2ab + b² to find 34².
19. 19.Use (a + b)² = a² + 2ab + b² to find 81².
20. 20.Use (a + b)² = a² + 2ab + b² to find 68².
21. 21.Use (a − b)² = a² − 2ab + b² to find 24².
22. 22.Use (a − b)² = a² − 2ab + b² to find 59².
23. 23.Use (a + b)² = a² + 2ab + b² to find 41².
24. 24.Find the value of x² − 2xy + y² when x = 11 and y = 5.
25. 25.Use (a + b)(a − b) = a² − b² to find 103 × 97.
26. 26.Use (a − b)² = a² − 2ab + b² to find 85².
27. 27.Use (a + b)(a − b) = a² − b² to find 93 × 87.
28. 28.If a − b = 2 and ab = 3, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 99².
30. 30.Use (a + b)(a − b) = a² − b² to find 91 × 89.
31. 31.Use (a + b)(a − b) = a² − b² to find 77 × 63.
32. 32.Find the value of x² + 2xy + y² when x = 13 and y = 11.
33. 33.If a + b = 15 and ab = 54, what is a² + b²?
34. 34.Find the value of x² − 2xy + y² when x = 15 and y = 3.
35. 35.Find the value of x² + 2xy + y² when x = 15 and y = 1.
36. 36.Use (a + b)(a − b) = a² − b² to find 41 × 39.
37. 37.Use (a + b)(a − b) = a² − b² to find 71 × 69.
38. 38.If a + b = 15 and ab = 56, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 94².
40. 40.Use (a + b)² = a² + 2ab + b² to find 27².

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