Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 245 · 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 41².
2. 2.Use (a + b)² = a² + 2ab + b² to find 68².
3. 3.Use (a + b)(a − b) = a² − b² to find 106 × 94.
4. 4.Use a² − b² = (a + b)(a − b) to find 44² − 37².
5. 5.Find the value of x² − y² when x = 3 and y = 1.
6. 6.Use (a − b)² = a² − 2ab + b² to find 37².
7. 7.Use (a + b)(a − b) = a² − b² to find 38 × 22.
8. 8.Use (a + b)(a − b) = a² − b² to find 103 × 97.
9. 9.Find the value of x² − 2xy + y² when x = 10 and y = 9.
10. 10.Find the value of x² − 2xy + y² when x = 5 and y = 1.
11. 11.Use (a − b)² = a² − 2ab + b² to find 19².
12. 12.Use (a + b)(a − b) = a² − b² to find 21 × 19.
13. 13.Use (a + b)(a − b) = a² − b² to find 93 × 87.
14. 14.Use (a − b)² = a² − 2ab + b² to find 11².
15. 15.Use (a + b)(a − b) = a² − b² to find 85 × 75.
16. 16.Find the value of x² + 2xy + y² when x = 15 and y = 11.
17. 17.Use (a + b)(a − b) = a² − b² to find 33 × 27.
18. 18.Use (a − b)² = a² − 2ab + b² to find 21².
19. 19.Find the value of x² − 2xy + y² when x = 13 and y = 7.
20. 20.Find the value of x² + 2xy + y² when x = 14 and y = 6.
21. 21.Use a² − b² = (a + b)(a − b) to find 77² − 51².
22. 22.Use (a + b)² = a² + 2ab + b² to find 24².
23. 23.Use (a − b)² = a² − 2ab + b² to find 25².
24. 24.Use (a + b)² = a² + 2ab + b² to find 28².
25. 25.Use a² − b² = (a + b)(a − b) to find 40² − 7².
26. 26.If a + b = 9 and ab = 8, what is a² + b²?
27. 27.If a + b = 14 and ab = 24, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 84² − 50².
29. 29.Use (a + b)² = a² + 2ab + b² to find 42².
30. 30.Use (a + b)² = a² + 2ab + b² to find 109².
31. 31.Use (a − b)² = a² − 2ab + b² to find 58².
32. 32.Use (a + b)(a − b) = a² − b² to find 25 × 15.
33. 33.Use (a + b)(a − b) = a² − b² to find 68 × 52.
34. 34.Use (a − b)² = a² − 2ab + b² to find 77².
35. 35.Use (a + b)² = a² + 2ab + b² to find 75².
36. 36.If a − b = 5 and ab = 84, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 102².
38. 38.Find the value of x² − y² when x = 4 and y = 3.
39. 39.Use (a − b)² = a² − 2ab + b² to find 39².
40. 40.Use (a + b)² = a² + 2ab + b² to find 34².

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