Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 20 · 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 46 × 34.
2. 2.Use (a + b)² = a² + 2ab + b² to find 84².
3. 3.Use (a + b)(a − b) = a² − b² to find 31 × 29.
4. 4.Use (a − b)² = a² − 2ab + b² to find 75².
5. 5.Use a² − b² = (a + b)(a − b) to find 42² − 18².
6. 6.Use (a − b)² = a² − 2ab + b² to find 29².
7. 7.Use (a − b)² = a² − 2ab + b² to find 96².
8. 8.Use (a + b)² = a² + 2ab + b² to find 47².
9. 9.Find the value of x² − 2xy + y² when x = 9 and y = 4.
10. 10.Use a² − b² = (a + b)(a − b) to find 49² − 38².
11. 11.Use (a + b)(a − b) = a² − b² to find 41 × 39.
12. 12.Use (a + b)(a − b) = a² − b² to find 56 × 44.
13. 13.Find the value of x² + 2xy + y² when x = 13 and y = 6.
14. 14.Use (a + b)(a − b) = a² − b² to find 76 × 64.
15. 15.Use a² − b² = (a + b)(a − b) to find 59² − 51².
16. 16.Find the value of x² − 2xy + y² when x = 11 and y = 3.
17. 17.Find the value of x² + 2xy + y² when x = 9 and y = 3.
18. 18.Use (a − b)² = a² − 2ab + b² to find 88².
19. 19.Use (a + b)² = a² + 2ab + b² to find 85².
20. 20.Use (a + b)² = a² + 2ab + b² to find 51².
21. 21.If a − b = 1 and ab = 2, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 93² − 45².
23. 23.Use (a − b)² = a² − 2ab + b² to find 49².
24. 24.Use (a − b)² = a² − 2ab + b² to find 19².
25. 25.Use (a + b)² = a² + 2ab + b² to find 31².
26. 26.If a + b = 3 and ab = 2, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 88² − 18².
28. 28.If a − b = 8 and ab = 9, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 51² − 31².
30. 30.If a + b = 7 and ab = 12, what is a² + b²?
31. 31.Find the value of x² − y² when x = 14 and y = 5.
32. 32.Use (a + b)(a − b) = a² − b² to find 42 × 38.
33. 33.Use (a + b)(a − b) = a² − b² to find 89 × 71.
34. 34.Use (a − b)² = a² − 2ab + b² to find 48².
35. 35.Use (a + b)² = a² + 2ab + b² to find 103².
36. 36.Use (a + b)² = a² + 2ab + b² to find 109².
37. 37.Use (a − b)² = a² − 2ab + b² to find 78².
38. 38.Use (a + b)² = a² + 2ab + b² to find 57².
39. 39.Use a² − b² = (a + b)(a − b) to find 28² − 10².
40. 40.Find the value of x² − 2xy + y² when x = 5 and y = 2.

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