Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 774 · 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.If a − b = 2 and ab = 8, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 79².
3. 3.Use a² − b² = (a + b)(a − b) to find 81² − 9².
4. 4.Find the value of x² + 2xy + y² when x = 9 and y = 2.
5. 5.Use a² − b² = (a + b)(a − b) to find 43² − 8².
6. 6.Use (a − b)² = a² − 2ab + b² to find 99².
7. 7.Use (a − b)² = a² − 2ab + b² to find 53².
8. 8.Use (a − b)² = a² − 2ab + b² to find 17².
9. 9.Use (a + b)(a − b) = a² − b² to find 89 × 71.
10. 10.Find the value of x² − y² when x = 7 and y = 1.
11. 11.If a + b = 9 and ab = 14, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 46².
13. 13.Find the value of x² + 2xy + y² when x = 13 and y = 7.
14. 14.Use (a + b)² = a² + 2ab + b² to find 55².
15. 15.Use a² − b² = (a + b)(a − b) to find 57² − 40².
16. 16.Find the value of x² − y² when x = 8 and y = 7.
17. 17.Use (a + b)² = a² + 2ab + b² to find 19².
18. 18.If a − b = 1 and ab = 2, what is a² + b²?
19. 19.Find the value of x² + 2xy + y² when x = 9 and y = 3.
20. 20.Use (a + b)² = a² + 2ab + b² to find 56².
21. 21.Use (a − b)² = a² − 2ab + b² to find 16².
22. 22.Use (a + b)² = a² + 2ab + b² to find 73².
23. 23.Use a² − b² = (a + b)(a − b) to find 41² − 21².
24. 24.If a + b = 19 and ab = 84, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 55² − 39².
26. 26.Use (a + b)(a − b) = a² − b² to find 97 × 83.
27. 27.Use a² − b² = (a + b)(a − b) to find 56² − 5².
28. 28.Use (a + b)(a − b) = a² − b² to find 26 × 14.
29. 29.If a + b = 3 and ab = 2, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 11².
31. 31.Use (a + b)(a − b) = a² − b² to find 32 × 28.
32. 32.Use a² − b² = (a + b)(a − b) to find 61² − 8².
33. 33.Use (a − b)² = a² − 2ab + b² to find 47².
34. 34.Use a² − b² = (a + b)(a − b) to find 65² − 39².
35. 35.Find the value of x² − y² when x = 5 and y = 3.
36. 36.If a + b = 21 and ab = 108, what is a² + b²?
37. 37.Find the value of x² + 2xy + y² when x = 15 and y = 8.
38. 38.If a + b = 4 and ab = 3, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 15².
40. 40.Use (a − b)² = a² − 2ab + b² to find 35².

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