Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 325 · 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 = 14 and y = 2.
2. 2.Use (a + b)² = a² + 2ab + b² to find 76².
3. 3.Use (a − b)² = a² − 2ab + b² to find 12².
4. 4.If a + b = 10 and ab = 24, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 93².
6. 6.Use (a − b)² = a² − 2ab + b² to find 18².
7. 7.Use (a − b)² = a² − 2ab + b² to find 97².
8. 8.Use (a − b)² = a² − 2ab + b² to find 34².
9. 9.If a + b = 19 and ab = 88, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 84².
11. 11.Use (a − b)² = a² − 2ab + b² to find 67².
12. 12.If a − b = 3 and ab = 4, what is a² + b²?
13. 13.If a + b = 7 and ab = 12, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 48².
15. 15.Find the value of x² + 2xy + y² when x = 10 and y = 6.
16. 16.Use (a + b)(a − b) = a² − b² to find 26 × 14.
17. 17.Use (a − b)² = a² − 2ab + b² to find 95².
18. 18.Use a² − b² = (a + b)(a − b) to find 66² − 58².
19. 19.If a + b = 11 and ab = 28, what is a² + b²?
20. 20.Find the value of x² − y² when x = 4 and y = 2.
21. 21.Use a² − b² = (a + b)(a − b) to find 57² − 9².
22. 22.Use (a − b)² = a² − 2ab + b² to find 76².
23. 23.Use (a + b)² = a² + 2ab + b² to find 89².
24. 24.Use (a + b)² = a² + 2ab + b² to find 54².
25. 25.If a − b = 2 and ab = 8, what is a² + b²?
26. 26.If a − b = 2 and ab = 3, what is a² + b²?
27. 27.Find the value of x² − y² when x = 7 and y = 1.
28. 28.Use a² − b² = (a + b)(a − b) to find 66² − 34².
29. 29.Use (a − b)² = a² − 2ab + b² to find 82².
30. 30.Find the value of x² − y² when x = 6 and y = 1.
31. 31.Use (a − b)² = a² − 2ab + b² to find 17².
32. 32.Use (a + b)(a − b) = a² − b² to find 102 × 98.
33. 33.Use (a − b)² = a² − 2ab + b² to find 13².
34. 34.Use (a + b)(a − b) = a² − b² to find 52 × 48.
35. 35.Use (a + b)(a − b) = a² − b² to find 94 × 86.
36. 36.Use a² − b² = (a + b)(a − b) to find 62² − 3².
37. 37.If a + b = 3 and ab = 2, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 29².
39. 39.Use (a + b)(a − b) = a² − b² to find 103 × 97.
40. 40.Use (a − b)² = a² − 2ab + b² to find 78².

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