Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 850 · 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 87².
2. 2.Use a² − b² = (a + b)(a − b) to find 73² − 70².
3. 3.If a + b = 9 and ab = 18, what is a² + b²?
4. 4.If a + b = 3 and ab = 2, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 43 × 37.
6. 6.If a − b = 2 and ab = 35, what is a² + b²?
7. 7.If a + b = 18 and ab = 72, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 80² − 22².
9. 9.If a + b = 14 and ab = 33, what is a² + b²?
10. 10.If a + b = 4 and ab = 3, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 68².
12. 12.Use (a − b)² = a² − 2ab + b² to find 91².
13. 13.Use (a + b)(a − b) = a² − b² to find 69 × 51.
14. 14.Use (a + b)(a − b) = a² − b² to find 42 × 38.
15. 15.Find the value of x² + 2xy + y² when x = 11 and y = 6.
16. 16.Use a² − b² = (a + b)(a − b) to find 33² − 6².
17. 17.Use (a + b)² = a² + 2ab + b² to find 57².
18. 18.Find the value of x² − y² when x = 15 and y = 9.
19. 19.Use (a + b)(a − b) = a² − b² to find 95 × 85.
20. 20.Use (a − b)² = a² − 2ab + b² to find 47².
21. 21.Use a² − b² = (a + b)(a − b) to find 42² − 1².
22. 22.If a − b = 6 and ab = 40, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 81².
24. 24.Use (a + b)² = a² + 2ab + b² to find 14².
25. 25.Use a² − b² = (a + b)(a − b) to find 43² − 11².
26. 26.Use a² − b² = (a + b)(a − b) to find 98² − 29².
27. 27.Use (a − b)² = a² − 2ab + b² to find 84².
28. 28.Use (a + b)² = a² + 2ab + b² to find 45².
29. 29.Use (a + b)(a − b) = a² − b² to find 21 × 19.
30. 30.Use (a + b)² = a² + 2ab + b² to find 99².
31. 31.Use (a − b)² = a² − 2ab + b² to find 34².
32. 32.If a − b = 1 and ab = 2, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 94 × 86.
34. 34.Find the value of x² − 2xy + y² when x = 4 and y = 1.
35. 35.Use (a + b)² = a² + 2ab + b² to find 21².
36. 36.If a + b = 13 and ab = 36, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 109 × 91.
38. 38.Use (a − b)² = a² − 2ab + b² to find 13².
39. 39.Find the value of x² + 2xy + y² when x = 11 and y = 7.
40. 40.Use a² − b² = (a + b)(a − b) to find 20² − 19².

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