Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 605 · 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)² = a² − 2ab + b² to find 48².
2. 2.Use a² − b² = (a + b)(a − b) to find 35² − 29².
3. 3.Use a² − b² = (a + b)(a − b) to find 76² − 13².
4. 4.If a − b = 1 and ab = 20, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 16².
6. 6.Use (a − b)² = a² − 2ab + b² to find 73².
7. 7.Use (a + b)² = a² + 2ab + b² to find 66².
8. 8.Use (a + b)(a − b) = a² − b² to find 99 × 81.
9. 9.Find the value of x² − 2xy + y² when x = 13 and y = 3.
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 78².
12. 12.Use (a − b)² = a² − 2ab + b² to find 61².
13. 13.Use (a + b)² = a² + 2ab + b² to find 24².
14. 14.Use a² − b² = (a + b)(a − b) to find 59² − 29².
15. 15.Use (a + b)² = a² + 2ab + b² to find 25².
16. 16.Use a² − b² = (a + b)(a − b) to find 38² − 6².
17. 17.Use (a − b)² = a² − 2ab + b² to find 68².
18. 18.Use (a + b)² = a² + 2ab + b² to find 87².
19. 19.Use (a + b)² = a² + 2ab + b² to find 23².
20. 20.Find the value of x² − 2xy + y² when x = 12 and y = 3.
21. 21.Use (a + b)² = a² + 2ab + b² to find 79².
22. 22.Use (a + b)² = a² + 2ab + b² to find 64².
23. 23.Find the value of x² − y² when x = 11 and y = 8.
24. 24.Use a² − b² = (a + b)(a − b) to find 85² − 84².
25. 25.Use (a − b)² = a² − 2ab + b² to find 72².
26. 26.Use (a + b)² = a² + 2ab + b² to find 103².
27. 27.Use (a − b)² = a² − 2ab + b² to find 28².
28. 28.Use a² − b² = (a + b)(a − b) to find 37² − 21².
29. 29.Use (a + b)(a − b) = a² − b² to find 107 × 93.
30. 30.Use a² − b² = (a + b)(a − b) to find 30² − 4².
31. 31.Use (a + b)² = a² + 2ab + b² to find 82².
32. 32.Use (a + b)(a − b) = a² − b² to find 87 × 73.
33. 33.Use (a − b)² = a² − 2ab + b² to find 25².
34. 34.If a − b = 10 and ab = 11, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 31².
36. 36.Use (a + b)² = a² + 2ab + b² to find 15².
37. 37.Use (a − b)² = a² − 2ab + b² to find 38².
38. 38.Use (a − b)² = a² − 2ab + b² to find 39².
39. 39.Find the value of x² + 2xy + y² when x = 15 and y = 9.
40. 40.Use (a − b)² = a² − 2ab + b² to find 21².

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