Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 667 · 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)(a − b) = a² − b² to find 27 × 13.
2. 2.Use (a − b)² = a² − 2ab + b² to find 33².
3. 3.Use (a + b)² = a² + 2ab + b² to find 45².
4. 4.If a − b = 1 and ab = 2, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 45².
6. 6.Find the value of x² − 2xy + y² when x = 8 and y = 1.
7. 7.Use (a + b)(a − b) = a² − b² to find 62 × 58.
8. 8.Use (a − b)² = a² − 2ab + b² to find 57².
9. 9.Use (a + b)² = a² + 2ab + b² to find 83².
10. 10.Use a² − b² = (a + b)(a − b) to find 28² − 25².
11. 11.Use a² − b² = (a + b)(a − b) to find 29² − 19².
12. 12.Use (a + b)² = a² + 2ab + b² to find 32².
13. 13.Use (a + b)(a − b) = a² − b² to find 84 × 76.
14. 14.Use (a − b)² = a² − 2ab + b² to find 41².
15. 15.Find the value of x² + 2xy + y² when x = 3 and y = 1.
16. 16.If a + b = 11 and ab = 18, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 27² − 18².
18. 18.Use (a + b)² = a² + 2ab + b² to find 18².
19. 19.Use (a + b)² = a² + 2ab + b² to find 17².
20. 20.Use (a + b)² = a² + 2ab + b² to find 55².
21. 21.Use (a + b)(a − b) = a² − b² to find 74 × 66.
22. 22.Use a² − b² = (a + b)(a − b) to find 71² − 66².
23. 23.Use (a + b)(a − b) = a² − b² to find 49 × 31.
24. 24.Use a² − b² = (a + b)(a − b) to find 48² − 36².
25. 25.Use (a + b)² = a² + 2ab + b² to find 22².
26. 26.Use (a + b)(a − b) = a² − b² to find 39 × 21.
27. 27.Use (a − b)² = a² − 2ab + b² to find 81².
28. 28.Use (a − b)² = a² − 2ab + b² to find 17².
29. 29.Use (a + b)² = a² + 2ab + b² to find 19².
30. 30.If a + b = 21 and ab = 110, what is a² + b²?
31. 31.If a + b = 8 and ab = 12, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 56² − 14².
33. 33.Use a² − b² = (a + b)(a − b) to find 53² − 42².
34. 34.Use (a + b)(a − b) = a² − b² to find 86 × 74.
35. 35.Use (a − b)² = a² − 2ab + b² to find 84².
36. 36.If a + b = 7 and ab = 10, what is a² + b²?
37. 37.Find the value of x² + 2xy + y² when x = 8 and y = 6.
38. 38.Find the value of x² − 2xy + y² when x = 4 and y = 2.
39. 39.Use (a + b)(a − b) = a² − b² to find 109 × 91.
40. 40.Use (a − b)² = a² − 2ab + b² to find 56².

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