Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 831 · 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 = 14 and ab = 48, what is a² + b²?
2. 2.If a + b = 8 and ab = 7, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 103 × 97.
4. 4.Find the value of x² + 2xy + y² when x = 10 and y = 3.
5. 5.Use (a + b)(a − b) = a² − b² to find 29 × 11.
6. 6.Use a² − b² = (a + b)(a − b) to find 83² − 19².
7. 7.Use (a + b)² = a² + 2ab + b² to find 42².
8. 8.Use (a − b)² = a² − 2ab + b² to find 65².
9. 9.Find the value of x² + 2xy + y² when x = 7 and y = 5.
10. 10.Use (a + b)² = a² + 2ab + b² to find 69².
11. 11.Use (a + b)² = a² + 2ab + b² to find 104².
12. 12.Find the value of x² + 2xy + y² when x = 13 and y = 11.
13. 13.Use (a − b)² = a² − 2ab + b² to find 62².
14. 14.Use (a + b)² = a² + 2ab + b² to find 103².
15. 15.Use (a − b)² = a² − 2ab + b² to find 77².
16. 16.Use (a + b)² = a² + 2ab + b² to find 56².
17. 17.Use (a + b)² = a² + 2ab + b² to find 12².
18. 18.Use a² − b² = (a + b)(a − b) to find 59² − 54².
19. 19.If a + b = 12 and ab = 35, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 23² − 5².
21. 21.Use a² − b² = (a + b)(a − b) to find 73² − 15².
22. 22.Use (a − b)² = a² − 2ab + b² to find 54².
23. 23.Use (a − b)² = a² − 2ab + b² to find 99².
24. 24.Use (a + b)(a − b) = a² − b² to find 28 × 12.
25. 25.Use (a + b)² = a² + 2ab + b² to find 46².
26. 26.Use a² − b² = (a + b)(a − b) to find 82² − 37².
27. 27.If a − b = 1 and ab = 2, what is a² + b²?
28. 28.If a + b = 8 and ab = 12, what is a² + b²?
29. 29.If a − b = 7 and ab = 18, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 83 × 77.
31. 31.Use a² − b² = (a + b)(a − b) to find 26² − 2².
32. 32.Find the value of x² + 2xy + y² when x = 3 and y = 2.
33. 33.Use (a − b)² = a² − 2ab + b² to find 32².
34. 34.Use a² − b² = (a + b)(a − b) to find 48² − 33².
35. 35.Use (a + b)² = a² + 2ab + b² to find 16².
36. 36.Use (a + b)(a − b) = a² − b² to find 106 × 94.
37. 37.Use (a + b)² = a² + 2ab + b² to find 55².
38. 38.Use a² − b² = (a + b)(a − b) to find 49² − 5².
39. 39.Find the value of x² + 2xy + y² when x = 13 and y = 2.
40. 40.Find the value of x² − y² when x = 4 and y = 2.

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