Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 503 · 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 61².
2. 2.Use (a + b)(a − b) = a² − b² to find 36 × 24.
3. 3.Use (a + b)² = a² + 2ab + b² to find 86².
4. 4.Use (a + b)² = a² + 2ab + b² to find 102².
5. 5.Use (a + b)² = a² + 2ab + b² to find 92².
6. 6.Use (a − b)² = a² − 2ab + b² to find 39².
7. 7.Find the value of x² + 2xy + y² when x = 11 and y = 9.
8. 8.Use a² − b² = (a + b)(a − b) to find 96² − 55².
9. 9.Use (a + b)² = a² + 2ab + b² to find 54².
10. 10.If a + b = 15 and ab = 36, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 44 × 36.
12. 12.Find the value of x² + 2xy + y² when x = 11 and y = 1.
13. 13.Find the value of x² + 2xy + y² when x = 9 and y = 6.
14. 14.Use (a + b)(a − b) = a² − b² to find 109 × 91.
15. 15.Use a² − b² = (a + b)(a − b) to find 20² − 17².
16. 16.Use (a + b)² = a² + 2ab + b² to find 12².
17. 17.Use (a + b)(a − b) = a² − b² to find 34 × 26.
18. 18.Use (a + b)² = a² + 2ab + b² to find 22².
19. 19.If a + b = 21 and ab = 108, what is a² + b²?
20. 20.Find the value of x² + 2xy + y² when x = 3 and y = 1.
21. 21.Use (a + b)(a − b) = a² − b² to find 65 × 55.
22. 22.Use (a − b)² = a² − 2ab + b² to find 77².
23. 23.Use (a − b)² = a² − 2ab + b² to find 14².
24. 24.Find the value of x² − y² when x = 9 and y = 1.
25. 25.If a − b = 6 and ab = 7, what is a² + b²?
26. 26.If a − b = 3 and ab = 108, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 82².
28. 28.Use (a + b)² = a² + 2ab + b² to find 103².
29. 29.Use (a − b)² = a² − 2ab + b² to find 88².
30. 30.Use (a − b)² = a² − 2ab + b² to find 45².
31. 31.Use (a + b)² = a² + 2ab + b² to find 85².
32. 32.Use a² − b² = (a + b)(a − b) to find 29² − 5².
33. 33.Use (a + b)(a − b) = a² − b² to find 77 × 63.
34. 34.Find the value of x² + 2xy + y² when x = 14 and y = 3.
35. 35.Use a² − b² = (a + b)(a − b) to find 95² − 39².
36. 36.Use a² − b² = (a + b)(a − b) to find 25² − 15².
37. 37.Find the value of x² − y² when x = 5 and y = 1.
38. 38.If a − b = 1 and ab = 2, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 32² − 26².
40. 40.Use (a + b)² = a² + 2ab + b² to find 78².

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