Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 802 · 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)(a − b) = a² − b² to find 75 × 65.
2. 2.Use a² − b² = (a + b)(a − b) to find 33² − 9².
3. 3.Use a² − b² = (a + b)(a − b) to find 40² − 27².
4. 4.Use (a − b)² = a² − 2ab + b² to find 47².
5. 5.Use (a − b)² = a² − 2ab + b² to find 13².
6. 6.Use (a + b)² = a² + 2ab + b² to find 41².
7. 7.If a − b = 4 and ab = 5, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 86².
9. 9.Use (a − b)² = a² − 2ab + b² to find 17².
10. 10.Use a² − b² = (a + b)(a − b) to find 65² − 30².
11. 11.Use (a + b)² = a² + 2ab + b² to find 59².
12. 12.Use a² − b² = (a + b)(a − b) to find 90² − 61².
13. 13.Use (a + b)² = a² + 2ab + b² to find 11².
14. 14.Use (a + b)² = a² + 2ab + b² to find 27².
15. 15.Use (a − b)² = a² − 2ab + b² to find 23².
16. 16.Use a² − b² = (a + b)(a − b) to find 25² − 12².
17. 17.Use a² − b² = (a + b)(a − b) to find 52² − 46².
18. 18.Use (a + b)² = a² + 2ab + b² to find 78².
19. 19.Use (a + b)(a − b) = a² − b² to find 95 × 85.
20. 20.Use (a + b)(a − b) = a² − b² to find 54 × 46.
21. 21.Use (a + b)(a − b) = a² − b² to find 102 × 98.
22. 22.Use a² − b² = (a + b)(a − b) to find 28² − 2².
23. 23.Use a² − b² = (a + b)(a − b) to find 37² − 16².
24. 24.Find the value of x² + 2xy + y² when x = 11 and y = 4.
25. 25.Use (a + b)(a − b) = a² − b² to find 68 × 52.
26. 26.Use a² − b² = (a + b)(a − b) to find 65² − 33².
27. 27.Use a² − b² = (a + b)(a − b) to find 70² − 36².
28. 28.Find the value of x² − 2xy + y² when x = 9 and y = 1.
29. 29.If a − b = 1 and ab = 20, what is a² + b²?
30. 30.Find the value of x² − 2xy + y² when x = 3 and y = 1.
31. 31.Use a² − b² = (a + b)(a − b) to find 40² − 11².
32. 32.Use (a + b)² = a² + 2ab + b² to find 63².
33. 33.Use (a + b)(a − b) = a² − b² to find 103 × 97.
34. 34.Use (a + b)(a − b) = a² − b² to find 106 × 94.
35. 35.Use a² − b² = (a + b)(a − b) to find 34² − 10².
36. 36.If a − b = 1 and ab = 56, what is a² + b²?
37. 37.If a + b = 16 and ab = 55, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 61².
39. 39.Use a² − b² = (a + b)(a − b) to find 32² − 10².
40. 40.Use (a + b)(a − b) = a² − b² to find 34 × 26.

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