Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 583 · 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 21².
2. 2.Use (a + b)(a − b) = a² − b² to find 104 × 96.
3. 3.Use (a + b)² = a² + 2ab + b² to find 58².
4. 4.Find the value of x² + 2xy + y² when x = 8 and y = 3.
5. 5.Use (a − b)² = a² − 2ab + b² to find 63².
6. 6.Find the value of x² − 2xy + y² when x = 11 and y = 3.
7. 7.Use (a − b)² = a² − 2ab + b² to find 22².
8. 8.Use a² − b² = (a + b)(a − b) to find 52² − 30².
9. 9.Use (a + b)² = a² + 2ab + b² to find 69².
10. 10.Use (a + b)² = a² + 2ab + b² to find 65².
11. 11.If a + b = 5 and ab = 6, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 34² − 3².
13. 13.If a + b = 16 and ab = 63, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 28² − 4².
15. 15.Find the value of x² − 2xy + y² when x = 11 and y = 1.
16. 16.Use (a − b)² = a² − 2ab + b² to find 96².
17. 17.If a − b = 5 and ab = 36, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 69 × 51.
19. 19.Use a² − b² = (a + b)(a − b) to find 44² − 40².
20. 20.Use (a + b)(a − b) = a² − b² to find 32 × 28.
21. 21.Use (a − b)² = a² − 2ab + b² to find 95².
22. 22.Use (a + b)² = a² + 2ab + b² to find 107².
23. 23.Use (a + b)² = a² + 2ab + b² to find 26².
24. 24.If a + b = 7 and ab = 12, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 62².
26. 26.Use (a + b)² = a² + 2ab + b² to find 36².
27. 27.Use a² − b² = (a + b)(a − b) to find 56² − 30².
28. 28.Use a² − b² = (a + b)(a − b) to find 40² − 22².
29. 29.Use (a + b)(a − b) = a² − b² to find 68 × 52.
30. 30.Use (a − b)² = a² − 2ab + b² to find 14².
31. 31.Use a² − b² = (a + b)(a − b) to find 32² − 15².
32. 32.Use (a + b)(a − b) = a² − b² to find 26 × 14.
33. 33.Use a² − b² = (a + b)(a − b) to find 45² − 26².
34. 34.If a − b = 10 and ab = 11, what is a² + b²?
35. 35.Find the value of x² + 2xy + y² when x = 11 and y = 3.
36. 36.Use (a − b)² = a² − 2ab + b² to find 43².
37. 37.Use (a − b)² = a² − 2ab + b² to find 36².
38. 38.Use (a + b)² = a² + 2ab + b² to find 42².
39. 39.Use (a + b)² = a² + 2ab + b² to find 11².
40. 40.Find the value of x² + 2xy + y² when x = 12 and y = 5.

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