Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 295 · 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)(a − b) = a² − b² to find 24 × 16.
2. 2.Use a² − b² = (a + b)(a − b) to find 27² − 4².
3. 3.Use (a + b)² = a² + 2ab + b² to find 101².
4. 4.Use (a + b)(a − b) = a² − b² to find 104 × 96.
5. 5.Use a² − b² = (a + b)(a − b) to find 25² − 10².
6. 6.Find the value of x² + 2xy + y² when x = 10 and y = 9.
7. 7.Use (a + b)² = a² + 2ab + b² to find 62².
8. 8.If a − b = 9 and ab = 36, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 29² − 23².
10. 10.Use (a − b)² = a² − 2ab + b² to find 85².
11. 11.Find the value of x² − y² when x = 12 and y = 5.
12. 12.If a + b = 17 and ab = 70, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 87².
14. 14.Use (a + b)(a − b) = a² − b² to find 88 × 72.
15. 15.Find the value of x² + 2xy + y² when x = 6 and y = 2.
16. 16.Use (a + b)² = a² + 2ab + b² to find 35².
17. 17.Use (a − b)² = a² − 2ab + b² to find 77².
18. 18.Use a² − b² = (a + b)(a − b) to find 38² − 11².
19. 19.Use (a − b)² = a² − 2ab + b² to find 13².
20. 20.Find the value of x² − 2xy + y² when x = 4 and y = 1.
21. 21.If a + b = 19 and ab = 90, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 75².
23. 23.Use a² − b² = (a + b)(a − b) to find 96² − 21².
24. 24.Use (a + b)² = a² + 2ab + b² to find 61².
25. 25.Use (a − b)² = a² − 2ab + b² to find 31².
26. 26.If a − b = 1 and ab = 6, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 83 × 77.
28. 28.Use (a − b)² = a² − 2ab + b² to find 66².
29. 29.Find the value of x² − y² when x = 4 and y = 3.
30. 30.If a − b = 1 and ab = 12, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 93 × 87.
32. 32.Use (a + b)(a − b) = a² − b² to find 59 × 41.
33. 33.Use (a − b)² = a² − 2ab + b² to find 73².
34. 34.Use a² − b² = (a + b)(a − b) to find 27² − 3².
35. 35.Use (a − b)² = a² − 2ab + b² to find 54².
36. 36.Use (a − b)² = a² − 2ab + b² to find 58².
37. 37.Use (a + b)(a − b) = a² − b² to find 74 × 66.
38. 38.Use a² − b² = (a + b)(a − b) to find 62² − 44².
39. 39.If a + b = 15 and ab = 54, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 102².

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