Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 131 · 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 46².
2. 2.Use (a + b)² = a² + 2ab + b² to find 105².
3. 3.Use a² − b² = (a + b)(a − b) to find 43² − 6².
4. 4.Use (a + b)(a − b) = a² − b² to find 78 × 62.
5. 5.If a + b = 22 and ab = 120, what is a² + b²?
6. 6.If a + b = 18 and ab = 80, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 56².
8. 8.If a − b = 1 and ab = 6, what is a² + b²?
9. 9.Find the value of x² − y² when x = 6 and y = 4.
10. 10.Use (a − b)² = a² − 2ab + b² to find 49².
11. 11.Use (a − b)² = a² − 2ab + b² to find 27².
12. 12.Use (a − b)² = a² − 2ab + b² to find 43².
13. 13.Use (a − b)² = a² − 2ab + b² to find 69².
14. 14.Use (a − b)² = a² − 2ab + b² to find 58².
15. 15.Use (a + b)(a − b) = a² − b² to find 28 × 12.
16. 16.Find the value of x² − y² when x = 13 and y = 3.
17. 17.Use (a + b)² = a² + 2ab + b² to find 75².
18. 18.Use (a − b)² = a² − 2ab + b² to find 67².
19. 19.Use (a + b)² = a² + 2ab + b² to find 26².
20. 20.Use (a + b)² = a² + 2ab + b² to find 32².
21. 21.Use a² − b² = (a + b)(a − b) to find 99² − 34².
22. 22.Find the value of x² − y² when x = 9 and y = 5.
23. 23.Use (a + b)² = a² + 2ab + b² to find 48².
24. 24.Use (a + b)² = a² + 2ab + b² to find 65².
25. 25.Use (a + b)² = a² + 2ab + b² to find 19².
26. 26.Use (a + b)(a − b) = a² − b² to find 91 × 89.
27. 27.Use a² − b² = (a + b)(a − b) to find 38² − 12².
28. 28.Use a² − b² = (a + b)(a − b) to find 86² − 23².
29. 29.If a − b = 1 and ab = 2, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 70² − 58².
31. 31.If a − b = 6 and ab = 16, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 95².
33. 33.Use (a + b)² = a² + 2ab + b² to find 12².
34. 34.If a − b = 2 and ab = 3, what is a² + b²?
35. 35.Find the value of x² + 2xy + y² when x = 13 and y = 4.
36. 36.Use (a + b)² = a² + 2ab + b² to find 25².
37. 37.Use (a − b)² = a² − 2ab + b² to find 57².
38. 38.If a + b = 15 and ab = 50, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 37².
40. 40.Use (a − b)² = a² − 2ab + b² to find 53².

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