Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 983 · 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 37 × 23.
2. 2.Use (a + b)(a − b) = a² − b² to find 46 × 34.
3. 3.Use (a − b)² = a² − 2ab + b² to find 41².
4. 4.Use (a − b)² = a² − 2ab + b² to find 11².
5. 5.Use (a − b)² = a² − 2ab + b² to find 75².
6. 6.Use (a + b)² = a² + 2ab + b² to find 39².
7. 7.Use (a + b)² = a² + 2ab + b² to find 66².
8. 8.Use a² − b² = (a + b)(a − b) to find 77² − 1².
9. 9.Use (a + b)² = a² + 2ab + b² to find 103².
10. 10.Use (a + b)² = a² + 2ab + b² to find 86².
11. 11.Use (a − b)² = a² − 2ab + b² to find 58².
12. 12.Find the value of x² − 2xy + y² when x = 8 and y = 2.
13. 13.Use (a − b)² = a² − 2ab + b² to find 21².
14. 14.Find the value of x² − y² when x = 5 and y = 3.
15. 15.Use (a + b)(a − b) = a² − b² to find 31 × 29.
16. 16.Use (a + b)(a − b) = a² − b² to find 48 × 32.
17. 17.Find the value of x² − y² when x = 9 and y = 6.
18. 18.If a − b = 4 and ab = 21, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 91².
20. 20.Use (a + b)² = a² + 2ab + b² to find 57².
21. 21.Use (a + b)(a − b) = a² − b² to find 67 × 53.
22. 22.Use (a − b)² = a² − 2ab + b² to find 18².
23. 23.Use (a + b)² = a² + 2ab + b² to find 55².
24. 24.Use (a − b)² = a² − 2ab + b² to find 33².
25. 25.If a − b = 3 and ab = 70, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 83 × 77.
27. 27.Use (a − b)² = a² − 2ab + b² to find 47².
28. 28.If a + b = 15 and ab = 56, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 33 × 27.
30. 30.Use (a − b)² = a² − 2ab + b² to find 15².
31. 31.Use (a + b)² = a² + 2ab + b² to find 71².
32. 32.Find the value of x² − 2xy + y² when x = 12 and y = 5.
33. 33.Use (a + b)(a − b) = a² − b² to find 102 × 98.
34. 34.Use (a − b)² = a² − 2ab + b² to find 57².
35. 35.Use (a + b)² = a² + 2ab + b² to find 104².
36. 36.Use (a + b)² = a² + 2ab + b² to find 47².
37. 37.Use (a + b)² = a² + 2ab + b² to find 31².
38. 38.Find the value of x² − 2xy + y² when x = 8 and y = 1.
39. 39.Use a² − b² = (a + b)(a − b) to find 72² − 52².
40. 40.Use (a + b)² = a² + 2ab + b² to find 42².

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