Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 397 · 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 (a + b)(a − b) = a² − b² to find 87 × 73.
3. 3.Find the value of x² − y² when x = 14 and y = 11.
4. 4.Use (a + b)(a − b) = a² − b² to find 83 × 77.
5. 5.Use (a + b)(a − b) = a² − b² to find 106 × 94.
6. 6.Use a² − b² = (a + b)(a − b) to find 89² − 6².
7. 7.Use (a + b)² = a² + 2ab + b² to find 96².
8. 8.Use a² − b² = (a + b)(a − b) to find 24² − 15².
9. 9.Use (a + b)² = a² + 2ab + b² to find 64².
10. 10.Use (a + b)(a − b) = a² − b² to find 22 × 18.
11. 11.If a + b = 14 and ab = 33, what is a² + b²?
12. 12.If a + b = 13 and ab = 42, what is a² + b²?
13. 13.If a − b = 2 and ab = 15, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 102 × 98.
15. 15.Use a² − b² = (a + b)(a − b) to find 60² − 28².
16. 16.Use (a − b)² = a² − 2ab + b² to find 11².
17. 17.Find the value of x² − 2xy + y² when x = 12 and y = 11.
18. 18.Use (a − b)² = a² − 2ab + b² to find 36².
19. 19.Use (a + b)(a − b) = a² − b² to find 56 × 44.
20. 20.Find the value of x² − 2xy + y² when x = 4 and y = 1.
21. 21.Use (a + b)(a − b) = a² − b² to find 73 × 67.
22. 22.Use a² − b² = (a + b)(a − b) to find 20² − 18².
23. 23.If a − b = 1 and ab = 20, what is a² + b²?
24. 24.If a − b = 2 and ab = 35, what is a² + b²?
25. 25.If a + b = 10 and ab = 9, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 35².
27. 27.Find the value of x² + 2xy + y² when x = 9 and y = 8.
28. 28.Use a² − b² = (a + b)(a − b) to find 65² − 7².
29. 29.Use (a + b)² = a² + 2ab + b² to find 92².
30. 30.Find the value of x² − 2xy + y² when x = 14 and y = 3.
31. 31.Use (a + b)(a − b) = a² − b² to find 99 × 81.
32. 32.Find the value of x² + 2xy + y² when x = 12 and y = 7.
33. 33.Use (a + b)² = a² + 2ab + b² to find 85².
34. 34.Use a² − b² = (a + b)(a − b) to find 43² − 38².
35. 35.Use (a − b)² = a² − 2ab + b² to find 76².
36. 36.Use a² − b² = (a + b)(a − b) to find 48² − 46².
37. 37.If a + b = 5 and ab = 6, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 99².
39. 39.Use (a − b)² = a² − 2ab + b² to find 43².
40. 40.Find the value of x² + 2xy + y² when x = 15 and y = 13.

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