Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 407 · 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 a² − b² = (a + b)(a − b) to find 86² − 16².
2. 2.Use (a + b)(a − b) = a² − b² to find 79 × 61.
3. 3.Use (a + b)² = a² + 2ab + b² to find 14².
4. 4.Use (a + b)(a − b) = a² − b² to find 49 × 31.
5. 5.Use a² − b² = (a + b)(a − b) to find 89² − 87².
6. 6.If a + b = 9 and ab = 20, what is a² + b²?
7. 7.If a + b = 7 and ab = 12, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 27².
9. 9.Use (a − b)² = a² − 2ab + b² to find 72².
10. 10.Use (a + b)² = a² + 2ab + b² to find 94².
11. 11.Use a² − b² = (a + b)(a − b) to find 35² − 29².
12. 12.If a + b = 8 and ab = 15, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 62 × 58.
14. 14.Find the value of x² + 2xy + y² when x = 6 and y = 3.
15. 15.Use (a − b)² = a² − 2ab + b² to find 73².
16. 16.Use a² − b² = (a + b)(a − b) to find 73² − 11².
17. 17.Use (a + b)² = a² + 2ab + b² to find 38².
18. 18.If a + b = 13 and ab = 12, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 19².
20. 20.Use (a + b)² = a² + 2ab + b² to find 79².
21. 21.Use a² − b² = (a + b)(a − b) to find 54² − 3².
22. 22.Use (a + b)² = a² + 2ab + b² to find 96².
23. 23.Use (a + b)(a − b) = a² − b² to find 22 × 18.
24. 24.Find the value of x² + 2xy + y² when x = 9 and y = 4.
25. 25.Use a² − b² = (a + b)(a − b) to find 52² − 11².
26. 26.Use (a + b)² = a² + 2ab + b² to find 93².
27. 27.If a − b = 4 and ab = 12, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 89 × 71.
29. 29.Use a² − b² = (a + b)(a − b) to find 55² − 39².
30. 30.Use (a + b)² = a² + 2ab + b² to find 49².
31. 31.Use (a + b)² = a² + 2ab + b² to find 99².
32. 32.Use (a − b)² = a² − 2ab + b² to find 37².
33. 33.Use (a + b)(a − b) = a² − b² to find 33 × 27.
34. 34.Use a² − b² = (a + b)(a − b) to find 26² − 19².
35. 35.Use (a + b)(a − b) = a² − b² to find 104 × 96.
36. 36.Use (a + b)² = a² + 2ab + b² to find 39².
37. 37.Use (a − b)² = a² − 2ab + b² to find 78².
38. 38.Use (a − b)² = a² − 2ab + b² to find 47².
39. 39.If a + b = 7 and ab = 6, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 103².

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