Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 884 · 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 12².
2. 2.If a − b = 3 and ab = 10, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 71².
4. 4.Use (a − b)² = a² − 2ab + b² to find 17².
5. 5.Find the value of x² + 2xy + y² when x = 5 and y = 2.
6. 6.Use (a − b)² = a² − 2ab + b² to find 72².
7. 7.Use (a + b)² = a² + 2ab + b² to find 61².
8. 8.Use a² − b² = (a + b)(a − b) to find 69² − 44².
9. 9.If a − b = 2 and ab = 120, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 40² − 3².
11. 11.Use (a + b)(a − b) = a² − b² to find 88 × 72.
12. 12.Use (a − b)² = a² − 2ab + b² to find 97².
13. 13.Find the value of x² − 2xy + y² when x = 3 and y = 2.
14. 14.Find the value of x² + 2xy + y² when x = 11 and y = 7.
15. 15.Use a² − b² = (a + b)(a − b) to find 30² − 24².
16. 16.If a + b = 16 and ab = 55, what is a² + b²?
17. 17.If a − b = 1 and ab = 12, what is a² + b²?
18. 18.Find the value of x² + 2xy + y² when x = 15 and y = 12.
19. 19.Find the value of x² − 2xy + y² when x = 11 and y = 6.
20. 20.Use a² − b² = (a + b)(a − b) to find 39² − 6².
21. 21.Find the value of x² − y² when x = 5 and y = 4.
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 4.
23. 23.Use (a − b)² = a² − 2ab + b² to find 95².
24. 24.Find the value of x² − 2xy + y² when x = 8 and y = 2.
25. 25.If a − b = 2 and ab = 3, what is a² + b²?
26. 26.If a + b = 3 and ab = 2, what is a² + b²?
27. 27.If a + b = 11 and ab = 24, what is a² + b²?
28. 28.If a − b = 1 and ab = 20, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 22².
30. 30.Find the value of x² − 2xy + y² when x = 10 and y = 3.
31. 31.If a − b = 3 and ab = 28, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 26².
33. 33.Use (a − b)² = a² − 2ab + b² to find 59².
34. 34.Use (a + b)(a − b) = a² − b² to find 21 × 19.
35. 35.Find the value of x² − 2xy + y² when x = 7 and y = 2.
36. 36.Use a² − b² = (a + b)(a − b) to find 45² − 40².
37. 37.Use (a + b)² = a² + 2ab + b² to find 68².
38. 38.Use a² − b² = (a + b)(a − b) to find 84² − 11².
39. 39.Use (a + b)² = a² + 2ab + b² to find 19².
40. 40.Use (a + b)(a − b) = a² − b² to find 44 × 36.

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