Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 334 · 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 − y² when x = 4 and y = 2.
2. 2.Use (a + b)² = a² + 2ab + b² to find 16².
3. 3.Use a² − b² = (a + b)(a − b) to find 37² − 23².
4. 4.Use (a + b)² = a² + 2ab + b² to find 73².
5. 5.Use (a + b)(a − b) = a² − b² to find 54 × 46.
6. 6.If a − b = 3 and ab = 4, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 86².
8. 8.Use (a + b)² = a² + 2ab + b² to find 71².
9. 9.Use (a + b)² = a² + 2ab + b² to find 99².
10. 10.If a + b = 13 and ab = 42, what is a² + b²?
11. 11.If a + b = 8 and ab = 15, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 39 × 21.
13. 13.Use (a − b)² = a² − 2ab + b² to find 24².
14. 14.Use a² − b² = (a + b)(a − b) to find 63² − 21².
15. 15.Use a² − b² = (a + b)(a − b) to find 66² − 50².
16. 16.Use (a + b)² = a² + 2ab + b² to find 87².
17. 17.Use (a − b)² = a² − 2ab + b² to find 17².
18. 18.Use (a − b)² = a² − 2ab + b² to find 28².
19. 19.Use a² − b² = (a + b)(a − b) to find 34² − 20².
20. 20.Use (a + b)(a − b) = a² − b² to find 23 × 17.
21. 21.Find the value of x² + 2xy + y² when x = 15 and y = 1.
22. 22.Find the value of x² − 2xy + y² when x = 11 and y = 7.
23. 23.Find the value of x² − 2xy + y² when x = 4 and y = 1.
24. 24.Find the value of x² + 2xy + y² when x = 6 and y = 3.
25. 25.Use (a + b)(a − b) = a² − b² to find 73 × 67.
26. 26.Use (a + b)(a − b) = a² − b² to find 58 × 42.
27. 27.If a − b = 2 and ab = 3, what is a² + b²?
28. 28.Find the value of x² − y² when x = 15 and y = 3.
29. 29.Use (a + b)(a − b) = a² − b² to find 63 × 57.
30. 30.Use a² − b² = (a + b)(a − b) to find 60² − 33².
31. 31.Use (a − b)² = a² − 2ab + b² to find 87².
32. 32.Use a² − b² = (a + b)(a − b) to find 74² − 15².
33. 33.Use (a + b)(a − b) = a² − b² to find 42 × 38.
34. 34.If a − b = 1 and ab = 30, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 103².
36. 36.Use a² − b² = (a + b)(a − b) to find 43² − 18².
37. 37.If a − b = 6 and ab = 7, what is a² + b²?
38. 38.If a − b = 5 and ab = 66, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 48² − 32².
40. 40.Find the value of x² + 2xy + y² when x = 15 and y = 7.

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