Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 366 · 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.Find the value of x² − 2xy + y² when x = 9 and y = 7.
2. 2.If a − b = 5 and ab = 36, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 96² − 77².
4. 4.Find the value of x² + 2xy + y² when x = 10 and y = 2.
5. 5.Find the value of x² + 2xy + y² when x = 13 and y = 5.
6. 6.Use (a − b)² = a² − 2ab + b² to find 11².
7. 7.Use a² − b² = (a + b)(a − b) to find 39² − 21².
8. 8.Use (a + b)(a − b) = a² − b² to find 82 × 78.
9. 9.Find the value of x² + 2xy + y² when x = 15 and y = 1.
10. 10.Find the value of x² − 2xy + y² when x = 3 and y = 2.
11. 11.If a + b = 14 and ab = 33, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 82² − 4².
13. 13.Use a² − b² = (a + b)(a − b) to find 76² − 20².
14. 14.Use (a + b)² = a² + 2ab + b² to find 107².
15. 15.Use a² − b² = (a + b)(a − b) to find 42² − 21².
16. 16.Use (a + b)² = a² + 2ab + b² to find 34².
17. 17.Use (a − b)² = a² − 2ab + b² to find 53².
18. 18.Use (a + b)² = a² + 2ab + b² to find 93².
19. 19.If a + b = 12 and ab = 32, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 84 × 76.
21. 21.Use a² − b² = (a + b)(a − b) to find 70² − 56².
22. 22.Use (a − b)² = a² − 2ab + b² to find 69².
23. 23.Use (a + b)² = a² + 2ab + b² to find 95².
24. 24.Use (a − b)² = a² − 2ab + b² to find 99².
25. 25.Use (a + b)(a − b) = a² − b² to find 94 × 86.
26. 26.Use (a + b)(a − b) = a² − b² to find 69 × 51.
27. 27.If a + b = 10 and ab = 21, what is a² + b²?
28. 28.If a − b = 1 and ab = 2, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 75².
30. 30.Use (a + b)² = a² + 2ab + b² to find 69².
31. 31.If a + b = 16 and ab = 60, what is a² + b²?
32. 32.Find the value of x² − y² when x = 11 and y = 5.
33. 33.Use (a + b)(a − b) = a² − b² to find 39 × 21.
34. 34.Find the value of x² − 2xy + y² when x = 4 and y = 1.
35. 35.Use (a + b)² = a² + 2ab + b² to find 11².
36. 36.Use a² − b² = (a + b)(a − b) to find 30² − 24².
37. 37.If a + b = 12 and ab = 11, what is a² + b²?
38. 38.If a + b = 15 and ab = 56, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 87 × 73.
40. 40.Use a² − b² = (a + b)(a − b) to find 85² − 35².

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