Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 755 · 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 31².
2. 2.Use a² − b² = (a + b)(a − b) to find 65² − 56².
3. 3.If a + b = 16 and ab = 63, what is a² + b²?
4. 4.Find the value of x² − 2xy + y² when x = 5 and y = 1.
5. 5.Use (a − b)² = a² − 2ab + b² to find 12².
6. 6.Use (a + b)² = a² + 2ab + b² to find 75².
7. 7.If a + b = 11 and ab = 10, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 83².
9. 9.Use a² − b² = (a + b)(a − b) to find 53² − 20².
10. 10.Use a² − b² = (a + b)(a − b) to find 95² − 53².
11. 11.Find the value of x² − y² when x = 9 and y = 2.
12. 12.Find the value of x² − y² when x = 12 and y = 5.
13. 13.Use a² − b² = (a + b)(a − b) to find 88² − 61².
14. 14.Use (a + b)² = a² + 2ab + b² to find 81².
15. 15.Use (a + b)(a − b) = a² − b² to find 35 × 25.
16. 16.Use (a + b)² = a² + 2ab + b² to find 39².
17. 17.Use a² − b² = (a + b)(a − b) to find 65² − 32².
18. 18.Use a² − b² = (a + b)(a − b) to find 66² − 2².
19. 19.Use (a + b)(a − b) = a² − b² to find 109 × 91.
20. 20.Use a² − b² = (a + b)(a − b) to find 77² − 43².
21. 21.Use (a + b)² = a² + 2ab + b² to find 106².
22. 22.Use a² − b² = (a + b)(a − b) to find 43² − 8².
23. 23.Use (a + b)(a − b) = a² − b² to find 93 × 87.
24. 24.Use a² − b² = (a + b)(a − b) to find 33² − 18².
25. 25.Use a² − b² = (a + b)(a − b) to find 86² − 58².
26. 26.Find the value of x² − y² when x = 15 and y = 10.
27. 27.Use (a + b)² = a² + 2ab + b² to find 14².
28. 28.Use a² − b² = (a + b)(a − b) to find 43² − 40².
29. 29.Find the value of x² − 2xy + y² when x = 3 and y = 2.
30. 30.Use (a + b)(a − b) = a² − b² to find 76 × 64.
31. 31.Find the value of x² + 2xy + y² when x = 8 and y = 6.
32. 32.Find the value of x² + 2xy + y² when x = 11 and y = 1.
33. 33.Use (a − b)² = a² − 2ab + b² to find 21².
34. 34.If a + b = 3 and ab = 2, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 37 × 23.
36. 36.Use (a − b)² = a² − 2ab + b² to find 31².
37. 37.Use (a − b)² = a² − 2ab + b² to find 84².
38. 38.Use (a + b)² = a² + 2ab + b² to find 59².
39. 39.Use (a + b)² = a² + 2ab + b² to find 29².
40. 40.Use (a + b)(a − b) = a² − b² to find 23 × 17.

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