Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 946 · 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 a² − b² = (a + b)(a − b) to find 39² − 27².
2. 2.Find the value of x² − 2xy + y² when x = 5 and y = 1.
3. 3.Use (a + b)(a − b) = a² − b² to find 77 × 63.
4. 4.Use (a − b)² = a² − 2ab + b² to find 45².
5. 5.Use (a + b)² = a² + 2ab + b² to find 86².
6. 6.Use (a + b)² = a² + 2ab + b² to find 63².
7. 7.Use (a + b)(a − b) = a² − b² to find 86 × 74.
8. 8.Use (a − b)² = a² − 2ab + b² to find 12².
9. 9.Use (a − b)² = a² − 2ab + b² to find 31².
10. 10.If a + b = 8 and ab = 15, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 91².
12. 12.Use (a + b)² = a² + 2ab + b² to find 23².
13. 13.If a + b = 5 and ab = 4, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 77².
15. 15.If a + b = 9 and ab = 20, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 72².
17. 17.Use (a + b)(a − b) = a² − b² to find 21 × 19.
18. 18.Use (a − b)² = a² − 2ab + b² to find 75².
19. 19.Use (a + b)² = a² + 2ab + b² to find 41².
20. 20.Use a² − b² = (a + b)(a − b) to find 29² − 3².
21. 21.Use (a − b)² = a² − 2ab + b² to find 76².
22. 22.Use a² − b² = (a + b)(a − b) to find 68² − 18².
23. 23.Find the value of x² + 2xy + y² when x = 7 and y = 2.
24. 24.Use (a + b)(a − b) = a² − b² to find 55 × 45.
25. 25.Use (a − b)² = a² − 2ab + b² to find 32².
26. 26.Use a² − b² = (a + b)(a − b) to find 37² − 29².
27. 27.If a − b = 5 and ab = 14, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 87 × 73.
29. 29.Use (a + b)² = a² + 2ab + b² to find 57².
30. 30.Use (a − b)² = a² − 2ab + b² to find 39².
31. 31.Use a² − b² = (a + b)(a − b) to find 39² − 31².
32. 32.Use a² − b² = (a + b)(a − b) to find 62² − 36².
33. 33.Use (a + b)² = a² + 2ab + b² to find 53².
34. 34.Find the value of x² − 2xy + y² when x = 4 and y = 1.
35. 35.Use (a + b)(a − b) = a² − b² to find 89 × 71.
36. 36.Use (a + b)² = a² + 2ab + b² to find 16².
37. 37.Use (a + b)(a − b) = a² − b² to find 43 × 37.
38. 38.Use a² − b² = (a + b)(a − b) to find 56² − 23².
39. 39.Find the value of x² − 2xy + y² when x = 8 and y = 6.
40. 40.Use (a − b)² = a² − 2ab + b² to find 51².

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