Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 427 · 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.Find the value of x² − y² when x = 7 and y = 1.
2. 2.Use (a − b)² = a² − 2ab + b² to find 91².
3. 3.Use (a + b)² = a² + 2ab + b² to find 107².
4. 4.Use (a + b)² = a² + 2ab + b² to find 39².
5. 5.Find the value of x² − y² when x = 7 and y = 4.
6. 6.If a − b = 5 and ab = 24, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 52 × 48.
8. 8.If a − b = 4 and ab = 60, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 67².
10. 10.Use (a + b)² = a² + 2ab + b² to find 56².
11. 11.Use (a + b)² = a² + 2ab + b² to find 75².
12. 12.Use (a − b)² = a² − 2ab + b² to find 63².
13. 13.Find the value of x² − y² when x = 6 and y = 4.
14. 14.Use a² − b² = (a + b)(a − b) to find 43² − 7².
15. 15.Use a² − b² = (a + b)(a − b) to find 60² − 28².
16. 16.Use (a − b)² = a² − 2ab + b² to find 23².
17. 17.Use (a + b)² = a² + 2ab + b² to find 103².
18. 18.If a + b = 3 and ab = 2, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 42².
20. 20.Use (a + b)² = a² + 2ab + b² to find 35².
21. 21.If a − b = 1 and ab = 2, what is a² + b²?
22. 22.If a + b = 9 and ab = 8, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 97² − 78².
24. 24.Use (a + b)² = a² + 2ab + b² to find 14².
25. 25.Use (a + b)(a − b) = a² − b² to find 32 × 28.
26. 26.Use (a − b)² = a² − 2ab + b² to find 94².
27. 27.Use (a + b)(a − b) = a² − b² to find 106 × 94.
28. 28.Use (a + b)(a − b) = a² − b² to find 78 × 62.
29. 29.Use (a − b)² = a² − 2ab + b² to find 41².
30. 30.If a + b = 6 and ab = 5, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 57² − 7².
32. 32.Use a² − b² = (a + b)(a − b) to find 40² − 3².
33. 33.Use a² − b² = (a + b)(a − b) to find 75² − 38².
34. 34.Use (a + b)(a − b) = a² − b² to find 39 × 21.
35. 35.Use (a + b)(a − b) = a² − b² to find 41 × 39.
36. 36.If a − b = 3 and ab = 18, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 74².
38. 38.Use (a + b)² = a² + 2ab + b² to find 45².
39. 39.Use (a + b)(a − b) = a² − b² to find 81 × 79.
40. 40.Use (a − b)² = a² − 2ab + b² to find 68².

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