Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 339 · 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 31 × 29.
2. 2.Find the value of x² − y² when x = 15 and y = 14.
3. 3.Use (a − b)² = a² − 2ab + b² to find 61².
4. 4.Use (a + b)(a − b) = a² − b² to find 72 × 68.
5. 5.Use a² − b² = (a + b)(a − b) to find 99² − 7².
6. 6.Use (a − b)² = a² − 2ab + b² to find 13².
7. 7.Find the value of x² + 2xy + y² when x = 13 and y = 1.
8. 8.Find the value of x² + 2xy + y² when x = 6 and y = 5.
9. 9.Use (a + b)(a − b) = a² − b² to find 47 × 33.
10. 10.Use (a + b)² = a² + 2ab + b² to find 54².
11. 11.Find the value of x² + 2xy + y² when x = 12 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 30² − 8².
13. 13.Use a² − b² = (a + b)(a − b) to find 85² − 17².
14. 14.Use (a + b)² = a² + 2ab + b² to find 87².
15. 15.Find the value of x² + 2xy + y² when x = 10 and y = 7.
16. 16.Use (a − b)² = a² − 2ab + b² to find 44².
17. 17.Use (a + b)(a − b) = a² − b² to find 45 × 35.
18. 18.Use (a + b)² = a² + 2ab + b² to find 16².
19. 19.Use (a + b)² = a² + 2ab + b² to find 21².
20. 20.Use (a + b)² = a² + 2ab + b² to find 23².
21. 21.Use (a − b)² = a² − 2ab + b² to find 75².
22. 22.Use (a − b)² = a² − 2ab + b² to find 48².
23. 23.If a + b = 6 and ab = 8, what is a² + b²?
24. 24.If a + b = 7 and ab = 10, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 39² − 9².
26. 26.Use (a − b)² = a² − 2ab + b² to find 35².
27. 27.Find the value of x² − 2xy + y² when x = 6 and y = 5.
28. 28.Use a² − b² = (a + b)(a − b) to find 30² − 12².
29. 29.Use (a + b)(a − b) = a² − b² to find 61 × 59.
30. 30.If a − b = 2 and ab = 3, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 72².
32. 32.Use (a + b)² = a² + 2ab + b² to find 85².
33. 33.Use (a − b)² = a² − 2ab + b² to find 64².
34. 34.Use (a + b)² = a² + 2ab + b² to find 59².
35. 35.Use (a + b)² = a² + 2ab + b² to find 28².
36. 36.Use a² − b² = (a + b)(a − b) to find 73² − 22².
37. 37.Use (a + b)(a − b) = a² − b² to find 104 × 96.
38. 38.Use a² − b² = (a + b)(a − b) to find 30² − 22².
39. 39.Use (a − b)² = a² − 2ab + b² to find 77².
40. 40.Use (a + b)² = a² + 2ab + b² to find 108².

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