Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 731 · 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 a² − b² = (a + b)(a − b) to find 49² − 40².
2. 2.Use (a + b)(a − b) = a² − b² to find 42 × 38.
3. 3.Use (a + b)² = a² + 2ab + b² to find 19².
4. 4.Use (a + b)(a − b) = a² − b² to find 65 × 55.
5. 5.Use (a + b)² = a² + 2ab + b² to find 66².
6. 6.Find the value of x² − 2xy + y² when x = 5 and y = 1.
7. 7.Use a² − b² = (a + b)(a − b) to find 85² − 56².
8. 8.If a + b = 3 and ab = 2, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 90² − 20².
10. 10.Use (a + b)(a − b) = a² − b² to find 95 × 85.
11. 11.Use (a − b)² = a² − 2ab + b² to find 41².
12. 12.Use a² − b² = (a + b)(a − b) to find 37² − 35².
13. 13.If a + b = 11 and ab = 18, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 69² − 20².
15. 15.If a − b = 1 and ab = 12, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 67².
17. 17.Use (a + b)(a − b) = a² − b² to find 85 × 75.
18. 18.Use (a + b)² = a² + 2ab + b² to find 25².
19. 19.Use (a + b)² = a² + 2ab + b² to find 45².
20. 20.Use a² − b² = (a + b)(a − b) to find 25² − 18².
21. 21.Find the value of x² + 2xy + y² when x = 4 and y = 3.
22. 22.Use a² − b² = (a + b)(a − b) to find 47² − 7².
23. 23.Find the value of x² − y² when x = 5 and y = 1.
24. 24.Use (a − b)² = a² − 2ab + b² to find 47².
25. 25.If a + b = 13 and ab = 30, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 23².
27. 27.Use (a + b)(a − b) = a² − b² to find 22 × 18.
28. 28.Use (a − b)² = a² − 2ab + b² to find 92².
29. 29.Use (a + b)(a − b) = a² − b² to find 104 × 96.
30. 30.Use (a + b)(a − b) = a² − b² to find 64 × 56.
31. 31.Find the value of x² + 2xy + y² when x = 9 and y = 3.
32. 32.Use (a + b)(a − b) = a² − b² to find 84 × 76.
33. 33.Use (a + b)(a − b) = a² − b² to find 68 × 52.
34. 34.Use (a − b)² = a² − 2ab + b² to find 56².
35. 35.Use (a − b)² = a² − 2ab + b² to find 22².
36. 36.Use (a − b)² = a² − 2ab + b² to find 18².
37. 37.If a − b = 4 and ab = 60, what is a² + b²?
38. 38.Find the value of x² + 2xy + y² when x = 14 and y = 6.
39. 39.If a + b = 7 and ab = 6, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 69².

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