Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 54 · 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 13².
2. 2.Use a² − b² = (a + b)(a − b) to find 70² − 50².
3. 3.Use (a + b)(a − b) = a² − b² to find 87 × 73.
4. 4.If a − b = 1 and ab = 132, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 71².
6. 6.Use (a − b)² = a² − 2ab + b² to find 31².
7. 7.Use (a + b)² = a² + 2ab + b² to find 39².
8. 8.Use (a + b)² = a² + 2ab + b² to find 73².
9. 9.Use (a + b)(a − b) = a² − b² to find 71 × 69.
10. 10.Use (a + b)(a − b) = a² − b² to find 82 × 78.
11. 11.Find the value of x² − 2xy + y² when x = 3 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 49² − 13².
13. 13.Use (a + b)(a − b) = a² − b² to find 77 × 63.
14. 14.Use (a + b)(a − b) = a² − b² to find 91 × 89.
15. 15.If a − b = 3 and ab = 40, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 22 × 18.
17. 17.Use (a + b)² = a² + 2ab + b² to find 24².
18. 18.Use (a + b)² = a² + 2ab + b² to find 85².
19. 19.Find the value of x² − 2xy + y² when x = 14 and y = 2.
20. 20.Find the value of x² − y² when x = 4 and y = 2.
21. 21.Find the value of x² − y² when x = 9 and y = 1.
22. 22.Find the value of x² + 2xy + y² when x = 10 and y = 1.
23. 23.If a + b = 8 and ab = 15, what is a² + b²?
24. 24.Find the value of x² − 2xy + y² when x = 11 and y = 1.
25. 25.Use a² − b² = (a + b)(a − b) to find 44² − 16².
26. 26.Use (a + b)(a − b) = a² − b² to find 92 × 88.
27. 27.Use (a + b)² = a² + 2ab + b² to find 14².
28. 28.Use (a + b)² = a² + 2ab + b² to find 15².
29. 29.Use (a + b)² = a² + 2ab + b² to find 91².
30. 30.If a + b = 3 and ab = 2, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 82² − 65².
32. 32.Use (a − b)² = a² − 2ab + b² to find 27².
33. 33.Use (a + b)(a − b) = a² − b² to find 58 × 42.
34. 34.Find the value of x² − y² when x = 4 and y = 1.
35. 35.Use a² − b² = (a + b)(a − b) to find 66² − 41².
36. 36.Find the value of x² + 2xy + y² when x = 14 and y = 2.
37. 37.Use (a + b)(a − b) = a² − b² to find 46 × 34.
38. 38.Use (a + b)² = a² + 2ab + b² to find 45².
39. 39.Use (a − b)² = a² − 2ab + b² to find 17².
40. 40.Use (a + b)(a − b) = a² − b² to find 72 × 68.

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