Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 540 · 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)² = a² + 2ab + b² to find 41².
2. 2.Use (a + b)² = a² + 2ab + b² to find 81².
3. 3.Use (a + b)² = a² + 2ab + b² to find 91².
4. 4.Use (a + b)(a − b) = a² − b² to find 42 × 38.
5. 5.Use (a + b)(a − b) = a² − b² to find 44 × 36.
6. 6.Use (a − b)² = a² − 2ab + b² to find 84².
7. 7.If a + b = 8 and ab = 15, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 17².
9. 9.Use (a − b)² = a² − 2ab + b² to find 56².
10. 10.Use a² − b² = (a + b)(a − b) to find 28² − 14².
11. 11.Use (a − b)² = a² − 2ab + b² to find 82².
12. 12.Use (a + b)(a − b) = a² − b² to find 73 × 67.
13. 13.Find the value of x² − y² when x = 10 and y = 3.
14. 14.Use (a − b)² = a² − 2ab + b² to find 38².
15. 15.Use a² − b² = (a + b)(a − b) to find 46² − 2².
16. 16.Use (a + b)(a − b) = a² − b² to find 53 × 47.
17. 17.Use a² − b² = (a + b)(a − b) to find 37² − 6².
18. 18.Find the value of x² − y² when x = 9 and y = 7.
19. 19.Use (a + b)² = a² + 2ab + b² to find 16².
20. 20.Use (a + b)² = a² + 2ab + b² to find 59².
21. 21.Use (a − b)² = a² − 2ab + b² to find 26².
22. 22.Find the value of x² + 2xy + y² when x = 5 and y = 4.
23. 23.If a − b = 2 and ab = 15, what is a² + b²?
24. 24.If a − b = 2 and ab = 3, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 31².
26. 26.Use a² − b² = (a + b)(a − b) to find 57² − 52².
27. 27.Use (a − b)² = a² − 2ab + b² to find 88².
28. 28.Use (a − b)² = a² − 2ab + b² to find 41².
29. 29.Use a² − b² = (a + b)(a − b) to find 60² − 52².
30. 30.Use (a − b)² = a² − 2ab + b² to find 63².
31. 31.Use a² − b² = (a + b)(a − b) to find 87² − 52².
32. 32.Use (a − b)² = a² − 2ab + b² to find 67².
33. 33.Use a² − b² = (a + b)(a − b) to find 33² − 6².
34. 34.If a + b = 5 and ab = 6, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 97² − 37².
36. 36.Use (a + b)(a − b) = a² − b² to find 104 × 96.
37. 37.Find the value of x² − y² when x = 8 and y = 5.
38. 38.Use (a + b)² = a² + 2ab + b² to find 46².
39. 39.Use (a − b)² = a² − 2ab + b² to find 44².
40. 40.Use (a − b)² = a² − 2ab + b² to find 78².

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