Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 206 · 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 a² − b² = (a + b)(a − b) to find 36² − 3².
2. 2.Use a² − b² = (a + b)(a − b) to find 30² − 7².
3. 3.If a + b = 16 and ab = 55, what is a² + b²?
4. 4.If a − b = 1 and ab = 2, what is a² + b²?
5. 5.If a + b = 10 and ab = 16, what is a² + b²?
6. 6.Find the value of x² − y² when x = 15 and y = 13.
7. 7.Use (a + b)² = a² + 2ab + b² to find 21².
8. 8.Use (a − b)² = a² − 2ab + b² to find 95².
9. 9.If a − b = 5 and ab = 6, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 89².
11. 11.If a + b = 5 and ab = 4, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 45² − 24².
13. 13.Use (a + b)(a − b) = a² − b² to find 38 × 22.
14. 14.Use (a − b)² = a² − 2ab + b² to find 91².
15. 15.Use (a − b)² = a² − 2ab + b² to find 19².
16. 16.Find the value of x² − y² when x = 8 and y = 2.
17. 17.Use (a − b)² = a² − 2ab + b² to find 43².
18. 18.If a − b = 11 and ab = 12, what is a² + b²?
19. 19.Find the value of x² − y² when x = 14 and y = 2.
20. 20.Use (a + b)(a − b) = a² − b² to find 48 × 32.
21. 21.If a + b = 12 and ab = 27, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 108².
23. 23.Use (a + b)(a − b) = a² − b² to find 61 × 59.
24. 24.Use (a − b)² = a² − 2ab + b² to find 45².
25. 25.Use (a + b)(a − b) = a² − b² to find 84 × 76.
26. 26.Use a² − b² = (a + b)(a − b) to find 25² − 8².
27. 27.Find the value of x² − y² when x = 4 and y = 3.
28. 28.Use (a − b)² = a² − 2ab + b² to find 11².
29. 29.Use a² − b² = (a + b)(a − b) to find 28² − 12².
30. 30.If a − b = 2 and ab = 35, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 75 × 65.
32. 32.Use (a + b)(a − b) = a² − b² to find 21 × 19.
33. 33.Use (a + b)² = a² + 2ab + b² to find 44².
34. 34.Use (a + b)² = a² + 2ab + b² to find 38².
35. 35.If a + b = 5 and ab = 6, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 38² − 11².
37. 37.If a + b = 8 and ab = 7, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 34² − 3².
39. 39.If a + b = 13 and ab = 12, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 29².

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