Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 789 · 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.Find the value of x² − 2xy + y² when x = 14 and y = 1.
2. 2.Find the value of x² − y² when x = 7 and y = 6.
3. 3.Use (a + b)² = a² + 2ab + b² to find 67².
4. 4.Use (a + b)(a − b) = a² − b² to find 47 × 33.
5. 5.Use a² − b² = (a + b)(a − b) to find 41² − 18².
6. 6.Use (a − b)² = a² − 2ab + b² to find 62².
7. 7.Use (a + b)(a − b) = a² − b² to find 71 × 69.
8. 8.Find the value of x² + 2xy + y² when x = 10 and y = 3.
9. 9.Use (a + b)² = a² + 2ab + b² to find 81².
10. 10.If a + b = 9 and ab = 14, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 43² − 3².
12. 12.Use (a − b)² = a² − 2ab + b² to find 68².
13. 13.Find the value of x² + 2xy + y² when x = 5 and y = 3.
14. 14.Use (a − b)² = a² − 2ab + b² to find 92².
15. 15.Use (a + b)² = a² + 2ab + b² to find 76².
16. 16.Use (a − b)² = a² − 2ab + b² to find 26².
17. 17.If a + b = 15 and ab = 50, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 25² − 22².
19. 19.Use (a + b)² = a² + 2ab + b² to find 48².
20. 20.Use (a + b)(a − b) = a² − b² to find 28 × 12.
21. 21.If a + b = 3 and ab = 2, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 21².
23. 23.If a − b = 6 and ab = 7, what is a² + b²?
24. 24.If a + b = 4 and ab = 3, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 90² − 82².
26. 26.Use (a + b)² = a² + 2ab + b² to find 98².
27. 27.Use a² − b² = (a + b)(a − b) to find 66² − 35².
28. 28.Find the value of x² − 2xy + y² when x = 14 and y = 4.
29. 29.Use a² − b² = (a + b)(a − b) to find 32² − 1².
30. 30.Find the value of x² − 2xy + y² when x = 5 and y = 2.
31. 31.Find the value of x² − y² when x = 3 and y = 1.
32. 32.If a − b = 2 and ab = 3, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 34² − 26².
34. 34.Use (a + b)² = a² + 2ab + b² to find 38².
35. 35.Use (a + b)² = a² + 2ab + b² to find 87².
36. 36.Find the value of x² − y² when x = 4 and y = 2.
37. 37.Use (a + b)(a − b) = a² − b² to find 76 × 64.
38. 38.Use (a + b)² = a² + 2ab + b² to find 63².
39. 39.Use a² − b² = (a + b)(a − b) to find 23² − 1².
40. 40.Use (a + b)² = a² + 2ab + b² to find 71².

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