Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 679 · 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 60² − 22².
2. 2.Use (a + b)² = a² + 2ab + b² to find 31².
3. 3.Use (a − b)² = a² − 2ab + b² to find 28².
4. 4.If a − b = 4 and ab = 12, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 61².
6. 6.Use a² − b² = (a + b)(a − b) to find 82² − 66².
7. 7.Use (a + b)² = a² + 2ab + b² to find 33².
8. 8.Use (a + b)² = a² + 2ab + b² to find 98².
9. 9.Use (a − b)² = a² − 2ab + b² to find 74².
10. 10.Use (a + b)² = a² + 2ab + b² to find 24².
11. 11.Use a² − b² = (a + b)(a − b) to find 21² − 3².
12. 12.Use a² − b² = (a + b)(a − b) to find 68² − 58².
13. 13.Find the value of x² + 2xy + y² when x = 14 and y = 3.
14. 14.Use (a + b)² = a² + 2ab + b² to find 59².
15. 15.If a + b = 7 and ab = 6, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 27 × 13.
17. 17.Find the value of x² − y² when x = 8 and y = 2.
18. 18.Use (a + b)(a − b) = a² − b² to find 37 × 23.
19. 19.Use (a + b)² = a² + 2ab + b² to find 65².
20. 20.Use (a + b)² = a² + 2ab + b² to find 63².
21. 21.Use a² − b² = (a + b)(a − b) to find 71² − 32².
22. 22.Use (a + b)² = a² + 2ab + b² to find 58².
23. 23.Use (a + b)(a − b) = a² − b² to find 44 × 36.
24. 24.Use (a + b)² = a² + 2ab + b² to find 45².
25. 25.Find the value of x² + 2xy + y² when x = 4 and y = 3.
26. 26.Find the value of x² − y² when x = 15 and y = 4.
27. 27.Find the value of x² − 2xy + y² when x = 14 and y = 2.
28. 28.Use (a − b)² = a² − 2ab + b² to find 89².
29. 29.If a − b = 1 and ab = 2, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 19².
31. 31.Use (a + b)² = a² + 2ab + b² to find 26².
32. 32.If a − b = 1 and ab = 6, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 83 × 77.
34. 34.Use (a + b)² = a² + 2ab + b² to find 61².
35. 35.If a − b = 5 and ab = 6, what is a² + b²?
36. 36.Find the value of x² − 2xy + y² when x = 10 and y = 8.
37. 37.Use (a − b)² = a² − 2ab + b² to find 47².
38. 38.Use a² − b² = (a + b)(a − b) to find 36² − 7².
39. 39.Use (a + b)(a − b) = a² − b² to find 66 × 54.
40. 40.Use a² − b² = (a + b)(a − b) to find 80² − 52².

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