Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 972 · 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 = 5 and ab = 6, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 49² − 31².
3. 3.Use (a − b)² = a² − 2ab + b² to find 63².
4. 4.If a − b = 9 and ab = 10, what is a² + b²?
5. 5.Find the value of x² − y² when x = 15 and y = 12.
6. 6.Use a² − b² = (a + b)(a − b) to find 98² − 90².
7. 7.Use (a + b)(a − b) = a² − b² to find 74 × 66.
8. 8.Find the value of x² + 2xy + y² when x = 9 and y = 3.
9. 9.Find the value of x² − 2xy + y² when x = 11 and y = 1.
10. 10.Use (a + b)² = a² + 2ab + b² to find 98².
11. 11.Use a² − b² = (a + b)(a − b) to find 85² − 67².
12. 12.Use (a − b)² = a² − 2ab + b² to find 34².
13. 13.Find the value of x² − 2xy + y² when x = 11 and y = 7.
14. 14.Use (a + b)(a − b) = a² − b² to find 38 × 22.
15. 15.Use a² − b² = (a + b)(a − b) to find 22² − 8².
16. 16.Use (a + b)(a − b) = a² − b² to find 41 × 39.
17. 17.Use (a + b)(a − b) = a² − b² to find 63 × 57.
18. 18.If a − b = 3 and ab = 54, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 97² − 22².
20. 20.Use (a − b)² = a² − 2ab + b² to find 53².
21. 21.Use (a − b)² = a² − 2ab + b² to find 55².
22. 22.Use (a − b)² = a² − 2ab + b² to find 88².
23. 23.Use (a − b)² = a² − 2ab + b² to find 84².
24. 24.Use (a + b)² = a² + 2ab + b² to find 36².
25. 25.Find the value of x² − y² when x = 10 and y = 8.
26. 26.Use a² − b² = (a + b)(a − b) to find 43² − 18².
27. 27.Use (a − b)² = a² − 2ab + b² to find 96².
28. 28.Find the value of x² − 2xy + y² when x = 6 and y = 5.
29. 29.Find the value of x² + 2xy + y² when x = 4 and y = 3.
30. 30.Find the value of x² + 2xy + y² when x = 9 and y = 5.
31. 31.Find the value of x² − y² when x = 5 and y = 1.
32. 32.If a − b = 1 and ab = 12, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 8 and y = 5.
34. 34.If a + b = 7 and ab = 12, what is a² + b²?
35. 35.Find the value of x² + 2xy + y² when x = 10 and y = 6.
36. 36.Use (a + b)(a − b) = a² − b² to find 45 × 35.
37. 37.Use (a + b)(a − b) = a² − b² to find 95 × 85.
38. 38.Use (a − b)² = a² − 2ab + b² to find 15².
39. 39.Use (a + b)(a − b) = a² − b² to find 61 × 59.
40. 40.Use (a + b)(a − b) = a² − b² to find 104 × 96.

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