Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 738 · 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 11².
2. 2.Find the value of x² + 2xy + y² when x = 4 and y = 2.
3. 3.Use (a + b)(a − b) = a² − b² to find 72 × 68.
4. 4.Find the value of x² + 2xy + y² when x = 4 and y = 1.
5. 5.Find the value of x² − y² when x = 14 and y = 6.
6. 6.If a − b = 6 and ab = 7, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 43².
8. 8.Use a² − b² = (a + b)(a − b) to find 40² − 4².
9. 9.Use a² − b² = (a + b)(a − b) to find 21² − 17².
10. 10.Use a² − b² = (a + b)(a − b) to find 75² − 73².
11. 11.Find the value of x² − 2xy + y² when x = 3 and y = 2.
12. 12.Find the value of x² + 2xy + y² when x = 4 and y = 3.
13. 13.Use (a − b)² = a² − 2ab + b² to find 76².
14. 14.If a − b = 1 and ab = 2, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 82² − 42².
16. 16.Use (a − b)² = a² − 2ab + b² to find 85².
17. 17.Find the value of x² − y² when x = 5 and y = 1.
18. 18.If a − b = 3 and ab = 10, what is a² + b²?
19. 19.Find the value of x² − y² when x = 12 and y = 5.
20. 20.Find the value of x² − y² when x = 4 and y = 3.
21. 21.If a + b = 17 and ab = 66, what is a² + b²?
22. 22.Find the value of x² − 2xy + y² when x = 15 and y = 6.
23. 23.Find the value of x² + 2xy + y² when x = 8 and y = 5.
24. 24.Use (a − b)² = a² − 2ab + b² to find 54².
25. 25.Use a² − b² = (a + b)(a − b) to find 46² − 9².
26. 26.Use a² − b² = (a + b)(a − b) to find 21² − 3².
27. 27.Use a² − b² = (a + b)(a − b) to find 68² − 21².
28. 28.Use (a + b)(a − b) = a² − b² to find 23 × 17.
29. 29.Use (a + b)(a − b) = a² − b² to find 95 × 85.
30. 30.Use (a − b)² = a² − 2ab + b² to find 22².
31. 31.Use (a + b)² = a² + 2ab + b² to find 12².
32. 32.Use (a + b)² = a² + 2ab + b² to find 101².
33. 33.Find the value of x² − y² when x = 15 and y = 4.
34. 34.Use (a − b)² = a² − 2ab + b² to find 55².
35. 35.Find the value of x² + 2xy + y² when x = 9 and y = 4.
36. 36.Use a² − b² = (a + b)(a − b) to find 87² − 50².
37. 37.Use (a + b)² = a² + 2ab + b² to find 88².
38. 38.Use a² − b² = (a + b)(a − b) to find 80² − 3².
39. 39.Find the value of x² + 2xy + y² when x = 14 and y = 2.
40. 40.Use a² − b² = (a + b)(a − b) to find 84² − 55².

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