Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 959 · 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 52 × 48.
2. 2.Use (a − b)² = a² − 2ab + b² to find 94².
3. 3.Use (a + b)² = a² + 2ab + b² to find 66².
4. 4.Use (a + b)² = a² + 2ab + b² to find 53².
5. 5.Use (a + b)² = a² + 2ab + b² to find 78².
6. 6.Use a² − b² = (a + b)(a − b) to find 50² − 2².
7. 7.Find the value of x² − y² when x = 5 and y = 1.
8. 8.Find the value of x² + 2xy + y² when x = 14 and y = 3.
9. 9.Use (a − b)² = a² − 2ab + b² to find 15².
10. 10.Use (a − b)² = a² − 2ab + b² to find 79².
11. 11.Use a² − b² = (a + b)(a − b) to find 76² − 40².
12. 12.Use a² − b² = (a + b)(a − b) to find 58² − 19².
13. 13.Use (a + b)² = a² + 2ab + b² to find 38².
14. 14.Find the value of x² − y² when x = 14 and y = 9.
15. 15.If a + b = 7 and ab = 12, what is a² + b²?
16. 16.If a + b = 11 and ab = 18, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 79 × 61.
18. 18.Use (a + b)² = a² + 2ab + b² to find 21².
19. 19.Use a² − b² = (a + b)(a − b) to find 72² − 66².
20. 20.If a + b = 21 and ab = 108, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 22 × 18.
22. 22.If a + b = 7 and ab = 10, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 32 × 28.
24. 24.Find the value of x² + 2xy + y² when x = 4 and y = 1.
25. 25.If a + b = 5 and ab = 6, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 20² − 5².
27. 27.Use (a + b)² = a² + 2ab + b² to find 18².
28. 28.Use (a + b)² = a² + 2ab + b² to find 26².
29. 29.Use (a + b)² = a² + 2ab + b² to find 45².
30. 30.Use a² − b² = (a + b)(a − b) to find 31² − 9².
31. 31.Use a² − b² = (a + b)(a − b) to find 45² − 4².
32. 32.Use (a − b)² = a² − 2ab + b² to find 11².
33. 33.Use (a − b)² = a² − 2ab + b² to find 48².
34. 34.Use a² − b² = (a + b)(a − b) to find 88² − 33².
35. 35.Use (a + b)(a − b) = a² − b² to find 98 × 82.
36. 36.Use (a + b)² = a² + 2ab + b² to find 102².
37. 37.Use (a + b)² = a² + 2ab + b² to find 106².
38. 38.Use (a − b)² = a² − 2ab + b² to find 61².
39. 39.Use (a − b)² = a² − 2ab + b² to find 24².
40. 40.Use a² − b² = (a + b)(a − b) to find 50² − 14².

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