Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 621 · 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)² = a² − 2ab + b² to find 41².
2. 2.Use a² − b² = (a + b)(a − b) to find 21² − 19².
3. 3.Use a² − b² = (a + b)(a − b) to find 61² − 8².
4. 4.If a + b = 13 and ab = 22, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 18².
6. 6.Use (a − b)² = a² − 2ab + b² to find 73².
7. 7.Use (a + b)² = a² + 2ab + b² to find 44².
8. 8.If a + b = 12 and ab = 35, what is a² + b²?
9. 9.Find the value of x² + 2xy + y² when x = 5 and y = 1.
10. 10.Use (a + b)² = a² + 2ab + b² to find 94².
11. 11.Use (a + b)² = a² + 2ab + b² to find 37².
12. 12.Find the value of x² + 2xy + y² when x = 6 and y = 5.
13. 13.Use (a + b)(a − b) = a² − b² to find 23 × 17.
14. 14.Use (a − b)² = a² − 2ab + b² to find 62².
15. 15.If a − b = 6 and ab = 40, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 78².
17. 17.Use (a + b)² = a² + 2ab + b² to find 36².
18. 18.Use (a + b)² = a² + 2ab + b² to find 109².
19. 19.Use a² − b² = (a + b)(a − b) to find 89² − 43².
20. 20.Find the value of x² − y² when x = 4 and y = 2.
21. 21.Use (a − b)² = a² − 2ab + b² to find 91².
22. 22.Find the value of x² − 2xy + y² when x = 6 and y = 3.
23. 23.Use (a − b)² = a² − 2ab + b² to find 11².
24. 24.Use (a + b)² = a² + 2ab + b² to find 99².
25. 25.Use a² − b² = (a + b)(a − b) to find 59² − 5².
26. 26.Use (a + b)² = a² + 2ab + b² to find 63².
27. 27.Use a² − b² = (a + b)(a − b) to find 76² − 63².
28. 28.Use (a − b)² = a² − 2ab + b² to find 18².
29. 29.Use (a + b)² = a² + 2ab + b² to find 93².
30. 30.Find the value of x² − 2xy + y² when x = 14 and y = 3.
31. 31.Use (a + b)² = a² + 2ab + b² to find 88².
32. 32.Use a² − b² = (a + b)(a − b) to find 28² − 10².
33. 33.Use a² − b² = (a + b)(a − b) to find 85² − 51².
34. 34.Use a² − b² = (a + b)(a − b) to find 43² − 31².
35. 35.Use (a − b)² = a² − 2ab + b² to find 56².
36. 36.Use a² − b² = (a + b)(a − b) to find 64² − 3².
37. 37.Use (a − b)² = a² − 2ab + b² to find 19².
38. 38.Use (a + b)² = a² + 2ab + b² to find 107².
39. 39.Use (a − b)² = a² − 2ab + b² to find 66².
40. 40.Use (a + b)² = a² + 2ab + b² to find 92².

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