Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 282 · 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)(a − b) = a² − b² to find 73 × 67.
2. 2.Use a² − b² = (a + b)(a − b) to find 64² − 25².
3. 3.Use a² − b² = (a + b)(a − b) to find 81² − 5².
4. 4.Use (a + b)(a − b) = a² − b² to find 25 × 15.
5. 5.Use (a + b)² = a² + 2ab + b² to find 101².
6. 6.Use (a − b)² = a² − 2ab + b² to find 23².
7. 7.If a + b = 14 and ab = 24, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 59².
9. 9.Use (a + b)² = a² + 2ab + b² to find 29².
10. 10.Find the value of x² + 2xy + y² when x = 6 and y = 5.
11. 11.Find the value of x² + 2xy + y² when x = 14 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 64² − 34².
13. 13.Find the value of x² + 2xy + y² when x = 11 and y = 6.
14. 14.Use (a + b)(a − b) = a² − b² to find 28 × 12.
15. 15.Use (a − b)² = a² − 2ab + b² to find 66².
16. 16.Use (a + b)(a − b) = a² − b² to find 43 × 37.
17. 17.Use (a − b)² = a² − 2ab + b² to find 79².
18. 18.If a + b = 8 and ab = 7, what is a² + b²?
19. 19.Find the value of x² − y² when x = 14 and y = 11.
20. 20.Use (a − b)² = a² − 2ab + b² to find 58².
21. 21.Use a² − b² = (a + b)(a − b) to find 29² − 6².
22. 22.Find the value of x² − 2xy + y² when x = 8 and y = 4.
23. 23.If a + b = 5 and ab = 4, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 46² − 28².
25. 25.Find the value of x² − y² when x = 5 and y = 3.
26. 26.Use (a − b)² = a² − 2ab + b² to find 15².
27. 27.Find the value of x² + 2xy + y² when x = 3 and y = 2.
28. 28.Find the value of x² + 2xy + y² when x = 10 and y = 8.
29. 29.Use (a + b)² = a² + 2ab + b² to find 64².
30. 30.Find the value of x² − 2xy + y² when x = 3 and y = 2.
31. 31.Use (a + b)² = a² + 2ab + b² to find 85².
32. 32.Use (a + b)² = a² + 2ab + b² to find 109².
33. 33.Use (a + b)² = a² + 2ab + b² to find 38².
34. 34.Find the value of x² − 2xy + y² when x = 5 and y = 4.
35. 35.Use a² − b² = (a + b)(a − b) to find 48² − 14².
36. 36.Use (a + b)² = a² + 2ab + b² to find 25².
37. 37.Use (a − b)² = a² − 2ab + b² to find 53².
38. 38.Use (a − b)² = a² − 2ab + b² to find 47².
39. 39.If a − b = 2 and ab = 120, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 102 × 98.

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