Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 120 · 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 25² − 19².
2. 2.Find the value of x² + 2xy + y² when x = 10 and y = 4.
3. 3.Use (a − b)² = a² − 2ab + b² to find 99².
4. 4.Use (a − b)² = a² − 2ab + b² to find 76².
5. 5.Use a² − b² = (a + b)(a − b) to find 27² − 17².
6. 6.Use (a + b)(a − b) = a² − b² to find 104 × 96.
7. 7.Use (a + b)(a − b) = a² − b² to find 57 × 43.
8. 8.Use (a + b)(a − b) = a² − b² to find 72 × 68.
9. 9.Use (a + b)² = a² + 2ab + b² to find 77².
10. 10.Find the value of x² − 2xy + y² when x = 9 and y = 2.
11. 11.Use (a + b)² = a² + 2ab + b² to find 51².
12. 12.Use (a + b)² = a² + 2ab + b² to find 36².
13. 13.Use (a − b)² = a² − 2ab + b² to find 18².
14. 14.Use a² − b² = (a + b)(a − b) to find 51² − 6².
15. 15.Use (a − b)² = a² − 2ab + b² to find 42².
16. 16.Use (a − b)² = a² − 2ab + b² to find 55².
17. 17.Use (a + b)(a − b) = a² − b² to find 21 × 19.
18. 18.Use (a + b)² = a² + 2ab + b² to find 78².
19. 19.Find the value of x² − 2xy + y² when x = 12 and y = 5.
20. 20.Use a² − b² = (a + b)(a − b) to find 36² − 3².
21. 21.If a + b = 10 and ab = 9, what is a² + b²?
22. 22.Find the value of x² + 2xy + y² when x = 12 and y = 9.
23. 23.Use (a + b)(a − b) = a² − b² to find 43 × 37.
24. 24.Use (a + b)(a − b) = a² − b² to find 67 × 53.
25. 25.If a + b = 11 and ab = 18, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 29².
27. 27.Use (a + b)(a − b) = a² − b² to find 105 × 95.
28. 28.Use (a − b)² = a² − 2ab + b² to find 28².
29. 29.Use a² − b² = (a + b)(a − b) to find 40² − 8².
30. 30.Use (a + b)(a − b) = a² − b² to find 79 × 61.
31. 31.Use (a − b)² = a² − 2ab + b² to find 22².
32. 32.Use (a + b)(a − b) = a² − b² to find 26 × 14.
33. 33.Use (a + b)² = a² + 2ab + b² to find 53².
34. 34.If a − b = 2 and ab = 35, what is a² + b²?
35. 35.If a − b = 10 and ab = 11, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 95 × 85.
37. 37.If a + b = 11 and ab = 30, what is a² + b²?
38. 38.If a + b = 9 and ab = 20, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 34² − 1².
40. 40.If a + b = 12 and ab = 27, what is a² + b²?

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