Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 214 · 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 66² − 38².
2. 2.Use a² − b² = (a + b)(a − b) to find 32² − 9².
3. 3.Use (a + b)² = a² + 2ab + b² to find 34².
4. 4.Use (a + b)(a − b) = a² − b² to find 106 × 94.
5. 5.Find the value of x² − 2xy + y² when x = 7 and y = 4.
6. 6.Use (a + b)² = a² + 2ab + b² to find 63².
7. 7.Use a² − b² = (a + b)(a − b) to find 58² − 18².
8. 8.Use (a + b)(a − b) = a² − b² to find 67 × 53.
9. 9.Use (a + b)² = a² + 2ab + b² to find 42².
10. 10.If a − b = 6 and ab = 72, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 89².
12. 12.Use a² − b² = (a + b)(a − b) to find 22² − 3².
13. 13.If a − b = 4 and ab = 32, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 30² − 29².
15. 15.If a − b = 3 and ab = 4, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 58².
17. 17.Use (a − b)² = a² − 2ab + b² to find 87².
18. 18.Use (a − b)² = a² − 2ab + b² to find 75².
19. 19.Use (a − b)² = a² − 2ab + b² to find 83².
20. 20.Use a² − b² = (a + b)(a − b) to find 38² − 10².
21. 21.Use a² − b² = (a + b)(a − b) to find 69² − 64².
22. 22.Use (a + b)² = a² + 2ab + b² to find 38².
23. 23.Use (a + b)(a − b) = a² − b² to find 109 × 91.
24. 24.Use (a − b)² = a² − 2ab + b² to find 71².
25. 25.Find the value of x² − y² when x = 7 and y = 5.
26. 26.Use (a + b)² = a² + 2ab + b² to find 35².
27. 27.If a − b = 8 and ab = 48, what is a² + b²?
28. 28.If a − b = 1 and ab = 110, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 47².
30. 30.Use (a + b)(a − b) = a² − b² to find 27 × 13.
31. 31.Use (a − b)² = a² − 2ab + b² to find 55².
32. 32.If a − b = 2 and ab = 24, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 38².
34. 34.Use (a − b)² = a² − 2ab + b² to find 68².
35. 35.Use a² − b² = (a + b)(a − b) to find 32² − 11².
36. 36.Use (a + b)(a − b) = a² − b² to find 64 × 56.
37. 37.Use (a + b)² = a² + 2ab + b² to find 85².
38. 38.Use (a − b)² = a² − 2ab + b² to find 37².
39. 39.Use (a + b)² = a² + 2ab + b² to find 21².
40. 40.Use (a + b)² = a² + 2ab + b² to find 86².

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