Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 479 · 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.If a + b = 15 and ab = 44, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 36².
3. 3.Use (a + b)² = a² + 2ab + b² to find 24².
4. 4.Use (a + b)² = a² + 2ab + b² to find 86².
5. 5.Use (a + b)(a − b) = a² − b² to find 105 × 95.
6. 6.If a − b = 1 and ab = 72, what is a² + b²?
7. 7.If a + b = 13 and ab = 36, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 42 × 38.
9. 9.Use (a + b)(a − b) = a² − b² to find 31 × 29.
10. 10.Use a² − b² = (a + b)(a − b) to find 42² − 4².
11. 11.Use a² − b² = (a + b)(a − b) to find 38² − 4².
12. 12.Use (a + b)² = a² + 2ab + b² to find 105².
13. 13.Use (a + b)(a − b) = a² − b² to find 93 × 87.
14. 14.Use a² − b² = (a + b)(a − b) to find 31² − 24².
15. 15.Use a² − b² = (a + b)(a − b) to find 48² − 47².
16. 16.Use (a − b)² = a² − 2ab + b² to find 37².
17. 17.Use (a + b)(a − b) = a² − b² to find 23 × 17.
18. 18.Use a² − b² = (a + b)(a − b) to find 80² − 51².
19. 19.Find the value of x² − y² when x = 14 and y = 13.
20. 20.Use (a − b)² = a² − 2ab + b² to find 31².
21. 21.If a + b = 3 and ab = 2, what is a² + b²?
22. 22.Find the value of x² − y² when x = 6 and y = 2.
23. 23.Use (a − b)² = a² − 2ab + b² to find 26².
24. 24.Use (a + b)² = a² + 2ab + b² to find 69².
25. 25.Use (a + b)(a − b) = a² − b² to find 84 × 76.
26. 26.Use (a − b)² = a² − 2ab + b² to find 58².
27. 27.If a − b = 1 and ab = 6, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 97 × 83.
29. 29.Use (a + b)(a − b) = a² − b² to find 26 × 14.
30. 30.Use (a + b)² = a² + 2ab + b² to find 38².
31. 31.Use (a + b)(a − b) = a² − b² to find 32 × 28.
32. 32.If a + b = 9 and ab = 20, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 14 and y = 7.
34. 34.Use a² − b² = (a + b)(a − b) to find 42² − 9².
35. 35.Use (a − b)² = a² − 2ab + b² to find 32².
36. 36.Find the value of x² + 2xy + y² when x = 6 and y = 2.
37. 37.Use a² − b² = (a + b)(a − b) to find 39² − 35².
38. 38.If a + b = 9 and ab = 8, what is a² + b²?
39. 39.Find the value of x² − y² when x = 5 and y = 3.
40. 40.Use (a + b)² = a² + 2ab + b² to find 74².

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