Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 6 · 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 = 4 and ab = 12, what is a² + b²?
2. 2.If a + b = 3 and ab = 2, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 54².
4. 4.Use (a + b)(a − b) = a² − b² to find 75 × 65.
5. 5.Find the value of x² − 2xy + y² when x = 9 and y = 4.
6. 6.Use (a + b)(a − b) = a² − b² to find 65 × 55.
7. 7.Use (a − b)² = a² − 2ab + b² to find 27².
8. 8.Use a² − b² = (a + b)(a − b) to find 29² − 14².
9. 9.Use (a + b)(a − b) = a² − b² to find 91 × 89.
10. 10.If a + b = 15 and ab = 50, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 94² − 63².
12. 12.Use a² − b² = (a + b)(a − b) to find 63² − 27².
13. 13.Use (a + b)² = a² + 2ab + b² to find 94².
14. 14.Use a² − b² = (a + b)(a − b) to find 88² − 86².
15. 15.If a + b = 8 and ab = 15, what is a² + b²?
16. 16.If a − b = 2 and ab = 8, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 64² − 10².
18. 18.Find the value of x² + 2xy + y² when x = 15 and y = 9.
19. 19.Use (a + b)² = a² + 2ab + b² to find 73².
20. 20.Use (a − b)² = a² − 2ab + b² to find 62².
21. 21.Use (a − b)² = a² − 2ab + b² to find 52².
22. 22.Use (a + b)² = a² + 2ab + b² to find 31².
23. 23.Use (a − b)² = a² − 2ab + b² to find 12².
24. 24.Use (a + b)² = a² + 2ab + b² to find 19².
25. 25.Use (a + b)² = a² + 2ab + b² to find 95².
26. 26.Use (a + b)² = a² + 2ab + b² to find 43².
27. 27.Use a² − b² = (a + b)(a − b) to find 28² − 26².
28. 28.Use a² − b² = (a + b)(a − b) to find 52² − 15².
29. 29.Use a² − b² = (a + b)(a − b) to find 74² − 69².
30. 30.Use (a + b)² = a² + 2ab + b² to find 78².
31. 31.Use (a + b)² = a² + 2ab + b² to find 11².
32. 32.Use (a − b)² = a² − 2ab + b² to find 72².
33. 33.Use a² − b² = (a + b)(a − b) to find 90² − 23².
34. 34.Use (a + b)² = a² + 2ab + b² to find 62².
35. 35.Use (a − b)² = a² − 2ab + b² to find 32².
36. 36.If a − b = 2 and ab = 3, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 41 × 39.
38. 38.Use (a − b)² = a² − 2ab + b² to find 19².
39. 39.Use (a − b)² = a² − 2ab + b² to find 28².
40. 40.Find the value of x² − 2xy + y² when x = 4 and y = 1.

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