Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 790 · 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 = 2, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 73².
3. 3.If a − b = 7 and ab = 18, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 57².
5. 5.Use a² − b² = (a + b)(a − b) to find 68² − 19².
6. 6.Use a² − b² = (a + b)(a − b) to find 51² − 13².
7. 7.Use (a + b)² = a² + 2ab + b² to find 23².
8. 8.If a − b = 4 and ab = 21, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 97².
10. 10.Use a² − b² = (a + b)(a − b) to find 24² − 3².
11. 11.Use (a − b)² = a² − 2ab + b² to find 28².
12. 12.Use (a + b)(a − b) = a² − b² to find 92 × 88.
13. 13.Use (a − b)² = a² − 2ab + b² to find 17².
14. 14.Use (a − b)² = a² − 2ab + b² to find 29².
15. 15.Use (a − b)² = a² − 2ab + b² to find 63².
16. 16.Use (a + b)(a − b) = a² − b² to find 38 × 22.
17. 17.Use (a + b)² = a² + 2ab + b² to find 92².
18. 18.If a + b = 4 and ab = 3, what is a² + b²?
19. 19.If a − b = 5 and ab = 50, what is a² + b²?
20. 20.Find the value of x² − y² when x = 11 and y = 9.
21. 21.Find the value of x² − y² when x = 3 and y = 1.
22. 22.If a − b = 1 and ab = 2, what is a² + b²?
23. 23.If a + b = 6 and ab = 8, what is a² + b²?
24. 24.If a − b = 6 and ab = 72, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 62² − 42².
26. 26.Use a² − b² = (a + b)(a − b) to find 31² − 4².
27. 27.Use a² − b² = (a + b)(a − b) to find 85² − 18².
28. 28.Use (a + b)(a − b) = a² − b² to find 46 × 34.
29. 29.If a + b = 7 and ab = 10, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 24 × 16.
31. 31.Use (a + b)(a − b) = a² − b² to find 93 × 87.
32. 32.Use (a + b)² = a² + 2ab + b² to find 58².
33. 33.Use (a + b)(a − b) = a² − b² to find 26 × 14.
34. 34.Use a² − b² = (a + b)(a − b) to find 35² − 12².
35. 35.Use (a + b)(a − b) = a² − b² to find 62 × 58.
36. 36.Find the value of x² + 2xy + y² when x = 4 and y = 1.
37. 37.If a − b = 2 and ab = 3, what is a² + b²?
38. 38.If a + b = 16 and ab = 48, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 58².
40. 40.Use (a + b)² = a² + 2ab + b² to find 93².

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