Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 862 · 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 73².
2. 2.Use (a − b)² = a² − 2ab + b² to find 12².
3. 3.Use a² − b² = (a + b)(a − b) to find 24² − 22².
4. 4.Use (a + b)(a − b) = a² − b² to find 43 × 37.
5. 5.Use a² − b² = (a + b)(a − b) to find 97² − 27².
6. 6.Use (a − b)² = a² − 2ab + b² to find 19².
7. 7.If a + b = 3 and ab = 2, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 55 × 45.
9. 9.Use (a + b)(a − b) = a² − b² to find 73 × 67.
10. 10.Use a² − b² = (a + b)(a − b) to find 91² − 17².
11. 11.Find the value of x² − 2xy + y² when x = 7 and y = 5.
12. 12.Use (a − b)² = a² − 2ab + b² to find 74².
13. 13.Use (a + b)(a − b) = a² − b² to find 84 × 76.
14. 14.Use (a − b)² = a² − 2ab + b² to find 66².
15. 15.Use (a + b)² = a² + 2ab + b² to find 96².
16. 16.If a + b = 10 and ab = 9, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 54².
18. 18.Use (a − b)² = a² − 2ab + b² to find 94².
19. 19.Use (a − b)² = a² − 2ab + b² to find 65².
20. 20.Find the value of x² − 2xy + y² when x = 12 and y = 6.
21. 21.Use (a + b)(a − b) = a² − b² to find 75 × 65.
22. 22.Use a² − b² = (a + b)(a − b) to find 38² − 17².
23. 23.Use (a + b)² = a² + 2ab + b² to find 95².
24. 24.Use a² − b² = (a + b)(a − b) to find 51² − 46².
25. 25.If a + b = 4 and ab = 3, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 53 × 47.
27. 27.Find the value of x² − y² when x = 5 and y = 2.
28. 28.Use a² − b² = (a + b)(a − b) to find 83² − 37².
29. 29.Use a² − b² = (a + b)(a − b) to find 38² − 18².
30. 30.Use a² − b² = (a + b)(a − b) to find 23² − 5².
31. 31.Find the value of x² + 2xy + y² when x = 8 and y = 2.
32. 32.Use (a − b)² = a² − 2ab + b² to find 36².
33. 33.Use a² − b² = (a + b)(a − b) to find 57² − 9².
34. 34.Use (a + b)² = a² + 2ab + b² to find 18².
35. 35.Use (a + b)² = a² + 2ab + b² to find 63².
36. 36.Use (a − b)² = a² − 2ab + b² to find 26².
37. 37.Find the value of x² − y² when x = 7 and y = 1.
38. 38.Use (a − b)² = a² − 2ab + b² to find 89².
39. 39.Use (a + b)² = a² + 2ab + b² to find 42².
40. 40.Use (a + b)² = a² + 2ab + b² to find 88².

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