Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 178 · 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 = 3 and ab = 4, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 75².
3. 3.Use (a − b)² = a² − 2ab + b² to find 65².
4. 4.Use a² − b² = (a + b)(a − b) to find 51² − 49².
5. 5.Use a² − b² = (a + b)(a − b) to find 51² − 20².
6. 6.Use a² − b² = (a + b)(a − b) to find 27² − 20².
7. 7.Use a² − b² = (a + b)(a − b) to find 40² − 27².
8. 8.Use a² − b² = (a + b)(a − b) to find 81² − 61².
9. 9.Find the value of x² − y² when x = 7 and y = 1.
10. 10.Use (a + b)(a − b) = a² − b² to find 24 × 16.
11. 11.If a + b = 6 and ab = 8, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 76² − 51².
13. 13.Use (a − b)² = a² − 2ab + b² to find 82².
14. 14.If a + b = 3 and ab = 2, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 40² − 17².
16. 16.If a + b = 9 and ab = 20, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 69².
18. 18.Use (a − b)² = a² − 2ab + b² to find 38².
19. 19.Use a² − b² = (a + b)(a − b) to find 69² − 54².
20. 20.Use a² − b² = (a + b)(a − b) to find 69² − 29².
21. 21.If a + b = 9 and ab = 14, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 18².
23. 23.Use a² − b² = (a + b)(a − b) to find 99² − 1².
24. 24.Use (a − b)² = a² − 2ab + b² to find 43².
25. 25.Use a² − b² = (a + b)(a − b) to find 82² − 13².
26. 26.Use (a − b)² = a² − 2ab + b² to find 59².
27. 27.Find the value of x² − y² when x = 13 and y = 7.
28. 28.If a + b = 4 and ab = 3, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 96².
30. 30.Use (a + b)(a − b) = a² − b² to find 26 × 14.
31. 31.Use (a + b)(a − b) = a² − b² to find 95 × 85.
32. 32.Use (a − b)² = a² − 2ab + b² to find 51².
33. 33.Use (a + b)(a − b) = a² − b² to find 25 × 15.
34. 34.If a + b = 8 and ab = 15, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 62².
36. 36.Use (a + b)(a − b) = a² − b² to find 29 × 11.
37. 37.Find the value of x² − 2xy + y² when x = 4 and y = 3.
38. 38.Use (a − b)² = a² − 2ab + b² to find 53².
39. 39.Use (a − b)² = a² − 2ab + b² to find 39².
40. 40.Use a² − b² = (a + b)(a − b) to find 84² − 67².

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