Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 349 · 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 = 6 and ab = 5, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 95².
3. 3.Use (a − b)² = a² − 2ab + b² to find 43².
4. 4.Use (a + b)(a − b) = a² − b² to find 44 × 36.
5. 5.Use (a − b)² = a² − 2ab + b² to find 34².
6. 6.Use (a + b)² = a² + 2ab + b² to find 23².
7. 7.Use (a − b)² = a² − 2ab + b² to find 38².
8. 8.Find the value of x² + 2xy + y² when x = 3 and y = 1.
9. 9.Find the value of x² + 2xy + y² when x = 6 and y = 4.
10. 10.Find the value of x² − y² when x = 3 and y = 2.
11. 11.If a + b = 18 and ab = 77, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 55² − 21².
13. 13.Use (a − b)² = a² − 2ab + b² to find 35².
14. 14.Find the value of x² + 2xy + y² when x = 10 and y = 7.
15. 15.If a + b = 9 and ab = 14, what is a² + b²?
16. 16.If a + b = 3 and ab = 2, what is a² + b²?
17. 17.If a − b = 9 and ab = 22, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 39².
19. 19.Use a² − b² = (a + b)(a − b) to find 27² − 17².
20. 20.Find the value of x² − 2xy + y² when x = 3 and y = 2.
21. 21.Use (a + b)(a − b) = a² − b² to find 25 × 15.
22. 22.Use (a − b)² = a² − 2ab + b² to find 36².
23. 23.Use (a − b)² = a² − 2ab + b² to find 32².
24. 24.Use a² − b² = (a + b)(a − b) to find 40² − 8².
25. 25.Use (a + b)(a − b) = a² − b² to find 107 × 93.
26. 26.Use a² − b² = (a + b)(a − b) to find 56² − 14².
27. 27.Use a² − b² = (a + b)(a − b) to find 52² − 31².
28. 28.If a − b = 2 and ab = 3, what is a² + b²?
29. 29.If a − b = 2 and ab = 8, what is a² + b²?
30. 30.If a − b = 4 and ab = 12, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 94².
32. 32.Use (a − b)² = a² − 2ab + b² to find 69².
33. 33.If a − b = 4 and ab = 5, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 57 × 43.
35. 35.If a + b = 9 and ab = 8, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 66² − 19².
37. 37.Use (a − b)² = a² − 2ab + b² to find 58².
38. 38.Find the value of x² − 2xy + y² when x = 9 and y = 3.
39. 39.Use (a + b)(a − b) = a² − b² to find 43 × 37.
40. 40.If a − b = 7 and ab = 18, what is a² + b²?

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