Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 198 · 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 28² − 4².
2. 2.If a − b = 5 and ab = 14, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 73².
4. 4.Use a² − b² = (a + b)(a − b) to find 77² − 14².
5. 5.Use (a + b)(a − b) = a² − b² to find 66 × 54.
6. 6.Use a² − b² = (a + b)(a − b) to find 48² − 6².
7. 7.Use (a + b)² = a² + 2ab + b² to find 33².
8. 8.Find the value of x² + 2xy + y² when x = 15 and y = 2.
9. 9.Use (a − b)² = a² − 2ab + b² to find 96².
10. 10.Use (a + b)(a − b) = a² − b² to find 98 × 82.
11. 11.Use (a + b)(a − b) = a² − b² to find 95 × 85.
12. 12.Find the value of x² − 2xy + y² when x = 9 and y = 3.
13. 13.Use (a + b)² = a² + 2ab + b² to find 104².
14. 14.Use (a + b)² = a² + 2ab + b² to find 88².
15. 15.If a + b = 16 and ab = 48, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 69².
17. 17.Use (a + b)(a − b) = a² − b² to find 34 × 26.
18. 18.Use (a + b)² = a² + 2ab + b² to find 54².
19. 19.Use (a + b)² = a² + 2ab + b² to find 11².
20. 20.Use (a + b)² = a² + 2ab + b² to find 15².
21. 21.Find the value of x² + 2xy + y² when x = 14 and y = 6.
22. 22.If a − b = 5 and ab = 24, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 27² − 10².
24. 24.If a − b = 2 and ab = 3, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 108 × 92.
26. 26.Find the value of x² − y² when x = 6 and y = 5.
27. 27.Use (a − b)² = a² − 2ab + b² to find 21².
28. 28.Use (a + b)(a − b) = a² − b² to find 45 × 35.
29. 29.Find the value of x² − y² when x = 15 and y = 6.
30. 30.Use a² − b² = (a + b)(a − b) to find 31² − 27².
31. 31.If a + b = 5 and ab = 6, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 31².
33. 33.Use (a + b)² = a² + 2ab + b² to find 16².
34. 34.Use (a − b)² = a² − 2ab + b² to find 99².
35. 35.Use a² − b² = (a + b)(a − b) to find 55² − 43².
36. 36.Use (a + b)(a − b) = a² − b² to find 91 × 89.
37. 37.Find the value of x² − 2xy + y² when x = 3 and y = 1.
38. 38.Use (a − b)² = a² − 2ab + b² to find 15².
39. 39.Use (a − b)² = a² − 2ab + b² to find 89².
40. 40.Use (a + b)(a − b) = a² − b² to find 42 × 38.

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