Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 480 · 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.If a + b = 12 and ab = 20, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 56² − 32².
3. 3.Use (a + b)² = a² + 2ab + b² to find 102².
4. 4.Find the value of x² − 2xy + y² when x = 11 and y = 4.
5. 5.If a − b = 1 and ab = 12, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 63 × 57.
7. 7.Use a² − b² = (a + b)(a − b) to find 49² − 21².
8. 8.Use (a + b)(a − b) = a² − b² to find 73 × 67.
9. 9.Use (a + b)² = a² + 2ab + b² to find 22².
10. 10.Use a² − b² = (a + b)(a − b) to find 42² − 25².
11. 11.Use (a + b)² = a² + 2ab + b² to find 94².
12. 12.Use (a + b)(a − b) = a² − b² to find 88 × 72.
13. 13.If a + b = 16 and ab = 60, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 93² − 20².
15. 15.Use (a − b)² = a² − 2ab + b² to find 87².
16. 16.Use (a − b)² = a² − 2ab + b² to find 77².
17. 17.Use a² − b² = (a + b)(a − b) to find 56² − 23².
18. 18.Use (a + b)(a − b) = a² − b² to find 101 × 99.
19. 19.Use (a − b)² = a² − 2ab + b² to find 99².
20. 20.Use (a + b)(a − b) = a² − b² to find 42 × 38.
21. 21.Find the value of x² − 2xy + y² when x = 12 and y = 4.
22. 22.Find the value of x² − y² when x = 15 and y = 9.
23. 23.Find the value of x² − 2xy + y² when x = 3 and y = 2.
24. 24.Use a² − b² = (a + b)(a − b) to find 20² − 3².
25. 25.Use a² − b² = (a + b)(a − b) to find 73² − 23².
26. 26.Use (a + b)² = a² + 2ab + b² to find 67².
27. 27.Use (a − b)² = a² − 2ab + b² to find 22².
28. 28.Use a² − b² = (a + b)(a − b) to find 72² − 51².
29. 29.Use a² − b² = (a + b)(a − b) to find 60² − 8².
30. 30.Use (a + b)² = a² + 2ab + b² to find 31².
31. 31.If a + b = 3 and ab = 2, what is a² + b²?
32. 32.If a − b = 2 and ab = 8, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 37².
34. 34.Use (a + b)² = a² + 2ab + b² to find 42².
35. 35.Use a² − b² = (a + b)(a − b) to find 34² − 25².
36. 36.Use (a + b)² = a² + 2ab + b² to find 77².
37. 37.Use (a + b)² = a² + 2ab + b² to find 61².
38. 38.If a + b = 16 and ab = 48, what is a² + b²?
39. 39.If a + b = 4 and ab = 3, what is a² + b²?
40. 40.If a − b = 5 and ab = 14, what is a² + b²?

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