Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 819 · 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.If a − b = 7 and ab = 44, what is a² + b²?
2. 2.If a + b = 11 and ab = 24, what is a² + b²?
3. 3.Find the value of x² − 2xy + y² when x = 4 and y = 1.
4. 4.Use (a + b)² = a² + 2ab + b² to find 63².
5. 5.Use (a − b)² = a² − 2ab + b² to find 15².
6. 6.If a − b = 1 and ab = 6, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 26².
8. 8.Use a² − b² = (a + b)(a − b) to find 47² − 12².
9. 9.Use (a + b)(a − b) = a² − b² to find 84 × 76.
10. 10.Use a² − b² = (a + b)(a − b) to find 42² − 38².
11. 11.If a + b = 5 and ab = 4, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 94².
13. 13.Use (a + b)² = a² + 2ab + b² to find 93².
14. 14.If a + b = 13 and ab = 30, what is a² + b²?
15. 15.If a + b = 12 and ab = 32, what is a² + b²?
16. 16.If a + b = 17 and ab = 70, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 20² − 8².
18. 18.Use (a − b)² = a² − 2ab + b² to find 82².
19. 19.Use (a + b)² = a² + 2ab + b² to find 47².
20. 20.Use (a + b)(a − b) = a² − b² to find 25 × 15.
21. 21.Find the value of x² − 2xy + y² when x = 9 and y = 1.
22. 22.If a − b = 2 and ab = 3, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 39².
24. 24.Use (a + b)² = a² + 2ab + b² to find 81².
25. 25.Use (a + b)² = a² + 2ab + b² to find 104².
26. 26.Use a² − b² = (a + b)(a − b) to find 48² − 33².
27. 27.Use (a + b)(a − b) = a² − b² to find 97 × 83.
28. 28.Use (a + b)² = a² + 2ab + b² to find 25².
29. 29.Use (a + b)(a − b) = a² − b² to find 67 × 53.
30. 30.Use a² − b² = (a + b)(a − b) to find 74² − 66².
31. 31.Use (a − b)² = a² − 2ab + b² to find 54².
32. 32.Use (a − b)² = a² − 2ab + b² to find 75².
33. 33.Use (a + b)² = a² + 2ab + b² to find 107².
34. 34.Use a² − b² = (a + b)(a − b) to find 94² − 25².
35. 35.Use a² − b² = (a + b)(a − b) to find 74² − 24².
36. 36.Find the value of x² + 2xy + y² when x = 8 and y = 4.
37. 37.Use (a − b)² = a² − 2ab + b² to find 62².
38. 38.Use a² − b² = (a + b)(a − b) to find 73² − 56².
39. 39.Use a² − b² = (a + b)(a − b) to find 31² − 9².
40. 40.Use (a + b)² = a² + 2ab + b² to find 46².

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