Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 167 · 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 = 108, what is a² + b²?
2. 2.If a + b = 14 and ab = 48, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 38² − 19².
4. 4.Use a² − b² = (a + b)(a − b) to find 50² − 21².
5. 5.Find the value of x² + 2xy + y² when x = 12 and y = 3.
6. 6.If a + b = 5 and ab = 6, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 51².
8. 8.If a − b = 6 and ab = 40, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 68 × 52.
10. 10.Use (a + b)(a − b) = a² − b² to find 54 × 46.
11. 11.Use (a + b)(a − b) = a² − b² to find 102 × 98.
12. 12.Use (a + b)(a − b) = a² − b² to find 104 × 96.
13. 13.Find the value of x² − 2xy + y² when x = 5 and y = 4.
14. 14.Use a² − b² = (a + b)(a − b) to find 38² − 8².
15. 15.Use (a + b)² = a² + 2ab + b² to find 33².
16. 16.Use (a − b)² = a² − 2ab + b² to find 74².
17. 17.Use a² − b² = (a + b)(a − b) to find 56² − 9².
18. 18.If a + b = 6 and ab = 5, what is a² + b²?
19. 19.Use (a + b)(a − b) = a² − b² to find 77 × 63.
20. 20.Use (a + b)² = a² + 2ab + b² to find 97².
21. 21.Use a² − b² = (a + b)(a − b) to find 90² − 20².
22. 22.Use (a + b)² = a² + 2ab + b² to find 88².
23. 23.Use (a − b)² = a² − 2ab + b² to find 71².
24. 24.If a + b = 10 and ab = 16, what is a² + b²?
25. 25.If a − b = 1 and ab = 2, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 48² − 4².
27. 27.Find the value of x² + 2xy + y² when x = 4 and y = 2.
28. 28.Use (a + b)² = a² + 2ab + b² to find 27².
29. 29.Use (a − b)² = a² − 2ab + b² to find 11².
30. 30.Use (a + b)² = a² + 2ab + b² to find 19².
31. 31.If a + b = 9 and ab = 14, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 78².
33. 33.Use (a − b)² = a² − 2ab + b² to find 17².
34. 34.Use (a + b)² = a² + 2ab + b² to find 65².
35. 35.Use a² − b² = (a + b)(a − b) to find 87² − 68².
36. 36.If a − b = 10 and ab = 11, what is a² + b²?
37. 37.If a + b = 19 and ab = 90, what is a² + b²?
38. 38.Find the value of x² − 2xy + y² when x = 13 and y = 2.
39. 39.If a − b = 2 and ab = 48, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 72 × 68.

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