Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 973 · 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 62 × 58.
2. 2.Use (a + b)² = a² + 2ab + b² to find 24².
3. 3.Use (a + b)(a − b) = a² − b² to find 46 × 34.
4. 4.Use (a + b)² = a² + 2ab + b² to find 104².
5. 5.If a + b = 12 and ab = 20, what is a² + b²?
6. 6.Find the value of x² + 2xy + y² when x = 4 and y = 1.
7. 7.Use (a + b)(a − b) = a² − b² to find 43 × 37.
8. 8.Use (a + b)² = a² + 2ab + b² to find 31².
9. 9.Use (a + b)(a − b) = a² − b² to find 74 × 66.
10. 10.Use (a + b)(a − b) = a² − b² to find 87 × 73.
11. 11.Use (a − b)² = a² − 2ab + b² to find 75².
12. 12.If a + b = 10 and ab = 21, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 59² − 48².
14. 14.Use (a + b)(a − b) = a² − b² to find 73 × 67.
15. 15.Use (a + b)(a − b) = a² − b² to find 85 × 75.
16. 16.Use (a + b)(a − b) = a² − b² to find 63 × 57.
17. 17.Use (a + b)² = a² + 2ab + b² to find 99².
18. 18.Use (a − b)² = a² − 2ab + b² to find 84².
19. 19.Use (a + b)(a − b) = a² − b² to find 47 × 33.
20. 20.Use (a − b)² = a² − 2ab + b² to find 62².
21. 21.Use (a + b)² = a² + 2ab + b² to find 102².
22. 22.If a − b = 5 and ab = 6, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 108 × 92.
24. 24.Use (a + b)² = a² + 2ab + b² to find 21².
25. 25.Find the value of x² − 2xy + y² when x = 7 and y = 5.
26. 26.Use (a + b)² = a² + 2ab + b² to find 83².
27. 27.Use (a + b)² = a² + 2ab + b² to find 51².
28. 28.If a − b = 1 and ab = 6, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 76².
30. 30.Find the value of x² − 2xy + y² when x = 8 and y = 4.
31. 31.Use (a − b)² = a² − 2ab + b² to find 83².
32. 32.Use (a − b)² = a² − 2ab + b² to find 56².
33. 33.Use (a + b)² = a² + 2ab + b² to find 22².
34. 34.If a − b = 4 and ab = 5, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 29² − 28².
36. 36.If a + b = 8 and ab = 15, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 12².
38. 38.Use (a + b)(a − b) = a² − b² to find 109 × 91.
39. 39.If a + b = 3 and ab = 2, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 78².

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