Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 332 · 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.If a − b = 1 and ab = 2, what is a² + b²?
2. 2.If a + b = 12 and ab = 11, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 37².
4. 4.Find the value of x² − y² when x = 5 and y = 2.
5. 5.Use a² − b² = (a + b)(a − b) to find 37² − 7².
6. 6.Find the value of x² + 2xy + y² when x = 5 and y = 1.
7. 7.Find the value of x² − y² when x = 4 and y = 3.
8. 8.Use (a + b)(a − b) = a² − b² to find 32 × 28.
9. 9.Use (a + b)(a − b) = a² − b² to find 28 × 12.
10. 10.Use (a + b)(a − b) = a² − b² to find 44 × 36.
11. 11.Use (a + b)(a − b) = a² − b² to find 89 × 71.
12. 12.Use a² − b² = (a + b)(a − b) to find 86² − 78².
13. 13.Use (a − b)² = a² − 2ab + b² to find 67².
14. 14.Use (a + b)(a − b) = a² − b² to find 65 × 55.
15. 15.Use (a + b)² = a² + 2ab + b² to find 79².
16. 16.Use (a + b)² = a² + 2ab + b² to find 107².
17. 17.If a − b = 9 and ab = 36, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 83².
19. 19.Use (a + b)(a − b) = a² − b² to find 76 × 64.
20. 20.If a + b = 17 and ab = 70, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 35² − 3².
22. 22.Find the value of x² + 2xy + y² when x = 10 and y = 8.
23. 23.Find the value of x² − 2xy + y² when x = 14 and y = 4.
24. 24.Use (a + b)(a − b) = a² − b² to find 74 × 66.
25. 25.Use (a + b)(a − b) = a² − b² to find 57 × 43.
26. 26.Use (a − b)² = a² − 2ab + b² to find 69².
27. 27.Use (a + b)(a − b) = a² − b² to find 103 × 97.
28. 28.Use a² − b² = (a + b)(a − b) to find 31² − 10².
29. 29.Use (a + b)(a − b) = a² − b² to find 83 × 77.
30. 30.Use (a − b)² = a² − 2ab + b² to find 66².
31. 31.Use (a + b)² = a² + 2ab + b² to find 104².
32. 32.Use a² − b² = (a + b)(a − b) to find 31² − 13².
33. 33.Use (a − b)² = a² − 2ab + b² to find 14².
34. 34.Use (a + b)² = a² + 2ab + b² to find 57².
35. 35.If a − b = 2 and ab = 63, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 93².
37. 37.Use a² − b² = (a + b)(a − b) to find 27² − 16².
38. 38.Use (a + b)² = a² + 2ab + b² to find 51².
39. 39.Use (a + b)² = a² + 2ab + b² to find 103².
40. 40.Use (a + b)² = a² + 2ab + b² to find 97².

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