Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 264 · 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 74².
2. 2.If a + b = 3 and ab = 2, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 86² − 15².
4. 4.If a − b = 2 and ab = 24, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 41² − 16².
6. 6.If a − b = 1 and ab = 42, what is a² + b²?
7. 7.If a − b = 7 and ab = 30, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 105 × 95.
9. 9.Use (a + b)(a − b) = a² − b² to find 49 × 31.
10. 10.Find the value of x² + 2xy + y² when x = 3 and y = 2.
11. 11.Use (a + b)² = a² + 2ab + b² to find 43².
12. 12.Use (a − b)² = a² − 2ab + b² to find 65².
13. 13.Use a² − b² = (a + b)(a − b) to find 29² − 10².
14. 14.Use a² − b² = (a + b)(a − b) to find 52² − 35².
15. 15.Use (a − b)² = a² − 2ab + b² to find 58².
16. 16.Use (a − b)² = a² − 2ab + b² to find 43².
17. 17.Use (a − b)² = a² − 2ab + b² to find 72².
18. 18.Find the value of x² − 2xy + y² when x = 5 and y = 1.
19. 19.Use (a − b)² = a² − 2ab + b² to find 53².
20. 20.Use (a − b)² = a² − 2ab + b² to find 38².
21. 21.Use (a + b)(a − b) = a² − b² to find 43 × 37.
22. 22.Use a² − b² = (a + b)(a − b) to find 40² − 3².
23. 23.Use a² − b² = (a + b)(a − b) to find 74² − 71².
24. 24.Use (a + b)(a − b) = a² − b² to find 39 × 21.
25. 25.If a + b = 6 and ab = 5, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 74² − 10².
27. 27.Use (a − b)² = a² − 2ab + b² to find 36².
28. 28.Use (a + b)(a − b) = a² − b² to find 51 × 49.
29. 29.Use a² − b² = (a + b)(a − b) to find 67² − 17².
30. 30.Use a² − b² = (a + b)(a − b) to find 21² − 8².
31. 31.If a + b = 5 and ab = 6, what is a² + b²?
32. 32.If a − b = 10 and ab = 11, what is a² + b²?
33. 33.Find the value of x² − 2xy + y² when x = 11 and y = 9.
34. 34.Find the value of x² + 2xy + y² when x = 11 and y = 4.
35. 35.Use (a − b)² = a² − 2ab + b² to find 26².
36. 36.If a + b = 5 and ab = 4, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 58 × 42.
38. 38.Use (a + b)(a − b) = a² − b² to find 27 × 13.
39. 39.Find the value of x² + 2xy + y² when x = 5 and y = 2.
40. 40.Use (a + b)² = a² + 2ab + b² to find 66².

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