Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 631 · 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 47².
2. 2.Use (a + b)² = a² + 2ab + b² to find 38².
3. 3.If a + b = 7 and ab = 10, what is a² + b²?
4. 4.Find the value of x² + 2xy + y² when x = 13 and y = 7.
5. 5.Use (a + b)(a − b) = a² − b² to find 106 × 94.
6. 6.If a + b = 9 and ab = 18, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 57².
8. 8.Use (a + b)(a − b) = a² − b² to find 21 × 19.
9. 9.Use (a + b)² = a² + 2ab + b² to find 59².
10. 10.Find the value of x² − y² when x = 5 and y = 4.
11. 11.Use (a + b)² = a² + 2ab + b² to find 82².
12. 12.Use a² − b² = (a + b)(a − b) to find 46² − 21².
13. 13.Use (a − b)² = a² − 2ab + b² to find 98².
14. 14.Use (a + b)(a − b) = a² − b² to find 79 × 61.
15. 15.If a − b = 3 and ab = 4, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 91².
17. 17.Use a² − b² = (a + b)(a − b) to find 70² − 3².
18. 18.Find the value of x² − 2xy + y² when x = 6 and y = 1.
19. 19.Use (a − b)² = a² − 2ab + b² to find 68².
20. 20.Use (a − b)² = a² − 2ab + b² to find 23².
21. 21.Use (a − b)² = a² − 2ab + b² to find 62².
22. 22.Use a² − b² = (a + b)(a − b) to find 53² − 41².
23. 23.Use (a + b)(a − b) = a² − b² to find 25 × 15.
24. 24.If a + b = 12 and ab = 11, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 6 and y = 5.
26. 26.Use (a − b)² = a² − 2ab + b² to find 78².
27. 27.Use (a − b)² = a² − 2ab + b² to find 96².
28. 28.Use (a − b)² = a² − 2ab + b² to find 86².
29. 29.Find the value of x² + 2xy + y² when x = 7 and y = 3.
30. 30.Use (a + b)(a − b) = a² − b² to find 42 × 38.
31. 31.Use (a − b)² = a² − 2ab + b² to find 81².
32. 32.Find the value of x² − y² when x = 15 and y = 12.
33. 33.Use a² − b² = (a + b)(a − b) to find 25² − 17².
34. 34.Use (a + b)(a − b) = a² − b² to find 109 × 91.
35. 35.If a + b = 3 and ab = 2, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 21².
37. 37.If a − b = 4 and ab = 5, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 33².
39. 39.Use a² − b² = (a + b)(a − b) to find 82² − 72².
40. 40.Use (a + b)² = a² + 2ab + b² to find 13².

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