Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 230 · 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 30² − 25².
2. 2.Use (a − b)² = a² − 2ab + b² to find 38².
3. 3.Use (a + b)(a − b) = a² − b² to find 104 × 96.
4. 4.If a + b = 7 and ab = 12, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 17².
6. 6.Find the value of x² − 2xy + y² when x = 3 and y = 1.
7. 7.Use (a + b)(a − b) = a² − b² to find 64 × 56.
8. 8.Use (a + b)² = a² + 2ab + b² to find 67².
9. 9.Use (a + b)² = a² + 2ab + b² to find 58².
10. 10.Use (a + b)(a − b) = a² − b² to find 72 × 68.
11. 11.Find the value of x² − y² when x = 4 and y = 3.
12. 12.If a + b = 19 and ab = 88, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 62² − 11².
14. 14.Find the value of x² + 2xy + y² when x = 9 and y = 4.
15. 15.Use (a + b)² = a² + 2ab + b² to find 12².
16. 16.Use (a + b)(a − b) = a² − b² to find 68 × 52.
17. 17.If a − b = 6 and ab = 72, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 36².
19. 19.Use (a + b)² = a² + 2ab + b² to find 64².
20. 20.Use a² − b² = (a + b)(a − b) to find 50² − 2².
21. 21.Use (a + b)(a − b) = a² − b² to find 65 × 55.
22. 22.Use (a − b)² = a² − 2ab + b² to find 79².
23. 23.Use (a + b)(a − b) = a² − b² to find 39 × 21.
24. 24.Use (a + b)(a − b) = a² − b² to find 81 × 79.
25. 25.Find the value of x² + 2xy + y² when x = 8 and y = 4.
26. 26.Use (a − b)² = a² − 2ab + b² to find 87².
27. 27.Use (a + b)² = a² + 2ab + b² to find 102².
28. 28.Use (a + b)(a − b) = a² − b² to find 21 × 19.
29. 29.Use a² − b² = (a + b)(a − b) to find 41² − 2².
30. 30.Find the value of x² − y² when x = 7 and y = 6.
31. 31.If a + b = 7 and ab = 10, what is a² + b²?
32. 32.If a + b = 5 and ab = 6, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 45 × 35.
34. 34.Use a² − b² = (a + b)(a − b) to find 73² − 39².
35. 35.Use (a + b)(a − b) = a² − b² to find 58 × 42.
36. 36.Use a² − b² = (a + b)(a − b) to find 28² − 5².
37. 37.Find the value of x² − y² when x = 9 and y = 4.
38. 38.Use (a + b)² = a² + 2ab + b² to find 72².
39. 39.If a + b = 3 and ab = 2, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 64² − 33².

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