Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 725 · 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 a² − b² = (a + b)(a − b) to find 38² − 28².
2. 2.If a − b = 2 and ab = 80, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 28².
4. 4.Use (a − b)² = a² − 2ab + b² to find 96².
5. 5.Find the value of x² + 2xy + y² when x = 13 and y = 5.
6. 6.Find the value of x² + 2xy + y² when x = 6 and y = 1.
7. 7.Find the value of x² − y² when x = 15 and y = 6.
8. 8.Use (a − b)² = a² − 2ab + b² to find 43².
9. 9.Find the value of x² − 2xy + y² when x = 7 and y = 5.
10. 10.Use (a + b)² = a² + 2ab + b² to find 37².
11. 11.Use (a − b)² = a² − 2ab + b² to find 58².
12. 12.Use (a + b)(a − b) = a² − b² to find 108 × 92.
13. 13.Use (a + b)(a − b) = a² − b² to find 57 × 43.
14. 14.Find the value of x² − 2xy + y² when x = 14 and y = 13.
15. 15.Use (a + b)² = a² + 2ab + b² to find 49².
16. 16.Use (a − b)² = a² − 2ab + b² to find 24².
17. 17.If a + b = 4 and ab = 3, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 31².
19. 19.Use a² − b² = (a + b)(a − b) to find 82² − 67².
20. 20.Use (a + b)² = a² + 2ab + b² to find 64².
21. 21.Use (a + b)² = a² + 2ab + b² to find 99².
22. 22.Use (a + b)(a − b) = a² − b² to find 99 × 81.
23. 23.Use a² − b² = (a + b)(a − b) to find 51² − 12².
24. 24.Use (a + b)(a − b) = a² − b² to find 88 × 72.
25. 25.Use a² − b² = (a + b)(a − b) to find 51² − 31².
26. 26.Find the value of x² + 2xy + y² when x = 5 and y = 2.
27. 27.Use a² − b² = (a + b)(a − b) to find 29² − 25².
28. 28.If a + b = 7 and ab = 6, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 62² − 29².
30. 30.If a − b = 1 and ab = 2, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 32 × 28.
32. 32.If a − b = 3 and ab = 4, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 69² − 53².
34. 34.Use (a + b)² = a² + 2ab + b² to find 17².
35. 35.Find the value of x² − 2xy + y² when x = 14 and y = 6.
36. 36.Use a² − b² = (a + b)(a − b) to find 49² − 46².
37. 37.Find the value of x² − y² when x = 8 and y = 4.
38. 38.Use (a + b)(a − b) = a² − b² to find 36 × 24.
39. 39.Use a² − b² = (a + b)(a − b) to find 44² − 4².
40. 40.Use a² − b² = (a + b)(a − b) to find 46² − 16².

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