Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 758 · 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 71² − 14².
2. 2.Use a² − b² = (a + b)(a − b) to find 46² − 6².
3. 3.Use a² − b² = (a + b)(a − b) to find 22² − 4².
4. 4.Find the value of x² + 2xy + y² when x = 3 and y = 2.
5. 5.Find the value of x² − 2xy + y² when x = 8 and y = 4.
6. 6.Use (a + b)(a − b) = a² − b² to find 51 × 49.
7. 7.Use (a − b)² = a² − 2ab + b² to find 18².
8. 8.Use (a + b)(a − b) = a² − b² to find 46 × 34.
9. 9.Use (a − b)² = a² − 2ab + b² to find 16².
10. 10.Use (a + b)² = a² + 2ab + b² to find 68².
11. 11.Use a² − b² = (a + b)(a − b) to find 63² − 1².
12. 12.Use (a + b)(a − b) = a² − b² to find 34 × 26.
13. 13.Use (a + b)² = a² + 2ab + b² to find 66².
14. 14.Use (a + b)² = a² + 2ab + b² to find 101².
15. 15.Use (a + b)(a − b) = a² − b² to find 54 × 46.
16. 16.Use (a + b)² = a² + 2ab + b² to find 63².
17. 17.Use (a + b)² = a² + 2ab + b² to find 11².
18. 18.Use a² − b² = (a + b)(a − b) to find 42² − 36².
19. 19.Use (a + b)(a − b) = a² − b² to find 68 × 52.
20. 20.If a + b = 16 and ab = 60, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 107 × 93.
22. 22.Use (a − b)² = a² − 2ab + b² to find 24².
23. 23.Use a² − b² = (a + b)(a − b) to find 63² − 23².
24. 24.Use (a + b)(a − b) = a² − b² to find 84 × 76.
25. 25.Use (a − b)² = a² − 2ab + b² to find 13².
26. 26.Use (a − b)² = a² − 2ab + b² to find 75².
27. 27.If a + b = 7 and ab = 6, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 99² − 57².
29. 29.Use a² − b² = (a + b)(a − b) to find 25² − 7².
30. 30.Use (a − b)² = a² − 2ab + b² to find 63².
31. 31.Use (a − b)² = a² − 2ab + b² to find 34².
32. 32.Use (a + b)(a − b) = a² − b² to find 92 × 88.
33. 33.Use (a + b)² = a² + 2ab + b² to find 106².
34. 34.Find the value of x² + 2xy + y² when x = 10 and y = 4.
35. 35.Use a² − b² = (a + b)(a − b) to find 65² − 5².
36. 36.Use a² − b² = (a + b)(a − b) to find 28² − 20².
37. 37.If a + b = 15 and ab = 56, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 45².
39. 39.Use (a + b)² = a² + 2ab + b² to find 48².
40. 40.Use (a + b)² = a² + 2ab + b² to find 88².

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