Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 804 · 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 (a + b)(a − b) = a² − b² to find 31 × 29.
2. 2.Find the value of x² − 2xy + y² when x = 4 and y = 1.
3. 3.Use (a − b)² = a² − 2ab + b² to find 13².
4. 4.Use (a − b)² = a² − 2ab + b² to find 29².
5. 5.Use a² − b² = (a + b)(a − b) to find 45² − 9².
6. 6.Find the value of x² − 2xy + y² when x = 9 and y = 7.
7. 7.Use a² − b² = (a + b)(a − b) to find 71² − 46².
8. 8.Find the value of x² − 2xy + y² when x = 5 and y = 4.
9. 9.If a + b = 17 and ab = 72, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 81².
11. 11.Use a² − b² = (a + b)(a − b) to find 96² − 6².
12. 12.Find the value of x² − 2xy + y² when x = 3 and y = 2.
13. 13.If a − b = 11 and ab = 12, what is a² + b²?
14. 14.If a + b = 3 and ab = 2, what is a² + b²?
15. 15.Find the value of x² + 2xy + y² when x = 4 and y = 3.
16. 16.Use a² − b² = (a + b)(a − b) to find 25² − 5².
17. 17.Use (a + b)² = a² + 2ab + b² to find 13².
18. 18.Use (a + b)² = a² + 2ab + b² to find 67².
19. 19.Use (a + b)(a − b) = a² − b² to find 37 × 23.
20. 20.Find the value of x² + 2xy + y² when x = 14 and y = 3.
21. 21.Use (a + b)(a − b) = a² − b² to find 51 × 49.
22. 22.Use a² − b² = (a + b)(a − b) to find 43² − 36².
23. 23.Use a² − b² = (a + b)(a − b) to find 37² − 32².
24. 24.Use (a + b)² = a² + 2ab + b² to find 93².
25. 25.Use a² − b² = (a + b)(a − b) to find 57² − 7².
26. 26.Use a² − b² = (a + b)(a − b) to find 79² − 12².
27. 27.Use (a − b)² = a² − 2ab + b² to find 83².
28. 28.Use a² − b² = (a + b)(a − b) to find 85² − 27².
29. 29.Find the value of x² + 2xy + y² when x = 6 and y = 3.
30. 30.Use (a + b)² = a² + 2ab + b² to find 92².
31. 31.Use (a + b)(a − b) = a² − b² to find 93 × 87.
32. 32.Find the value of x² − y² when x = 9 and y = 5.
33. 33.Use (a + b)(a − b) = a² − b² to find 44 × 36.
34. 34.Use (a − b)² = a² − 2ab + b² to find 88².
35. 35.Use (a + b)(a − b) = a² − b² to find 71 × 69.
36. 36.If a + b = 14 and ab = 48, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 46².
38. 38.Use a² − b² = (a + b)(a − b) to find 70² − 10².
39. 39.Use (a + b)(a − b) = a² − b² to find 24 × 16.
40. 40.Find the value of x² − y² when x = 15 and y = 13.

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