Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 610 · 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)(a − b) = a² − b² to find 107 × 93.
2. 2.Use (a + b)(a − b) = a² − b² to find 64 × 56.
3. 3.Use (a + b)² = a² + 2ab + b² to find 66².
4. 4.If a − b = 2 and ab = 3, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 31 × 29.
6. 6.Find the value of x² − y² when x = 7 and y = 1.
7. 7.Use (a + b)² = a² + 2ab + b² to find 21².
8. 8.If a + b = 15 and ab = 50, what is a² + b²?
9. 9.Find the value of x² − 2xy + y² when x = 5 and y = 3.
10. 10.Use (a + b)² = a² + 2ab + b² to find 57².
11. 11.Use (a − b)² = a² − 2ab + b² to find 19².
12. 12.Use (a − b)² = a² − 2ab + b² to find 16².
13. 13.Use (a + b)² = a² + 2ab + b² to find 93².
14. 14.If a − b = 6 and ab = 55, what is a² + b²?
15. 15.Find the value of x² − 2xy + y² when x = 5 and y = 1.
16. 16.Use a² − b² = (a + b)(a − b) to find 57² − 51².
17. 17.Find the value of x² + 2xy + y² when x = 13 and y = 12.
18. 18.Use a² − b² = (a + b)(a − b) to find 83² − 43².
19. 19.Use (a + b)(a − b) = a² − b² to find 95 × 85.
20. 20.Find the value of x² − 2xy + y² when x = 13 and y = 1.
21. 21.Find the value of x² − 2xy + y² when x = 13 and y = 4.
22. 22.Use (a − b)² = a² − 2ab + b² to find 32².
23. 23.Use (a − b)² = a² − 2ab + b² to find 66².
24. 24.Use a² − b² = (a + b)(a − b) to find 39² − 12².
25. 25.Use (a + b)² = a² + 2ab + b² to find 25².
26. 26.Use a² − b² = (a + b)(a − b) to find 25² − 19².
27. 27.Find the value of x² + 2xy + y² when x = 3 and y = 2.
28. 28.Use a² − b² = (a + b)(a − b) to find 26² − 1².
29. 29.Use (a − b)² = a² − 2ab + b² to find 52².
30. 30.Use (a + b)(a − b) = a² − b² to find 94 × 86.
31. 31.Use (a − b)² = a² − 2ab + b² to find 21².
32. 32.Use a² − b² = (a + b)(a − b) to find 62² − 12².
33. 33.Use (a + b)² = a² + 2ab + b² to find 65².
34. 34.Use a² − b² = (a + b)(a − b) to find 26² − 23².
35. 35.Use (a + b)² = a² + 2ab + b² to find 83².
36. 36.If a + b = 7 and ab = 12, what is a² + b²?
37. 37.Find the value of x² − y² when x = 15 and y = 9.
38. 38.Use a² − b² = (a + b)(a − b) to find 51² − 20².
39. 39.Use (a + b)(a − b) = a² − b² to find 24 × 16.
40. 40.Find the value of x² − y² when x = 10 and y = 3.

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