Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 103 · 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 21².
2. 2.Use (a + b)² = a² + 2ab + b² to find 98².
3. 3.If a + b = 6 and ab = 8, what is a² + b²?
4. 4.If a + b = 20 and ab = 99, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 51².
6. 6.Use (a + b)(a − b) = a² − b² to find 92 × 88.
7. 7.Use (a + b)² = a² + 2ab + b² to find 85².
8. 8.Find the value of x² − y² when x = 10 and y = 5.
9. 9.If a − b = 7 and ab = 8, what is a² + b²?
10. 10.Find the value of x² + 2xy + y² when x = 11 and y = 10.
11. 11.Use (a + b)² = a² + 2ab + b² to find 108².
12. 12.Use (a − b)² = a² − 2ab + b² to find 71².
13. 13.Find the value of x² + 2xy + y² when x = 15 and y = 5.
14. 14.Use (a − b)² = a² − 2ab + b² to find 13².
15. 15.If a − b = 7 and ab = 44, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 38².
17. 17.If a + b = 8 and ab = 15, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 107².
19. 19.Use a² − b² = (a + b)(a − b) to find 83² − 47².
20. 20.If a + b = 8 and ab = 12, what is a² + b²?
21. 21.Find the value of x² − y² when x = 11 and y = 3.
22. 22.Use a² − b² = (a + b)(a − b) to find 55² − 8².
23. 23.Use (a + b)(a − b) = a² − b² to find 65 × 55.
24. 24.If a − b = 9 and ab = 22, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 31².
26. 26.Find the value of x² − 2xy + y² when x = 13 and y = 4.
27. 27.Use (a + b)² = a² + 2ab + b² to find 41².
28. 28.Use (a + b)(a − b) = a² − b² to find 78 × 62.
29. 29.If a + b = 4 and ab = 3, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 88².
31. 31.Use (a − b)² = a² − 2ab + b² to find 59².
32. 32.Use a² − b² = (a + b)(a − b) to find 36² − 7².
33. 33.Use (a + b)² = a² + 2ab + b² to find 25².
34. 34.Use (a − b)² = a² − 2ab + b² to find 98².
35. 35.Use (a + b)(a − b) = a² − b² to find 41 × 39.
36. 36.Find the value of x² + 2xy + y² when x = 3 and y = 1.
37. 37.Use (a − b)² = a² − 2ab + b² to find 42².
38. 38.Use (a + b)² = a² + 2ab + b² to find 71².
39. 39.Use a² − b² = (a + b)(a − b) to find 38² − 1².
40. 40.Use a² − b² = (a + b)(a − b) to find 28² − 2².

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