Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 979 · 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 103 × 97.
2. 2.Use a² − b² = (a + b)(a − b) to find 40² − 4².
3. 3.Use (a + b)² = a² + 2ab + b² to find 95².
4. 4.If a + b = 14 and ab = 40, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 59².
6. 6.Use (a + b)² = a² + 2ab + b² to find 59².
7. 7.Find the value of x² + 2xy + y² when x = 14 and y = 12.
8. 8.Use (a − b)² = a² − 2ab + b² to find 67².
9. 9.Use (a − b)² = a² − 2ab + b² to find 28².
10. 10.Use (a − b)² = a² − 2ab + b² to find 82².
11. 11.Use (a − b)² = a² − 2ab + b² to find 23².
12. 12.Use (a + b)(a − b) = a² − b² to find 44 × 36.
13. 13.Use (a + b)² = a² + 2ab + b² to find 39².
14. 14.If a − b = 1 and ab = 6, what is a² + b²?
15. 15.If a − b = 1 and ab = 72, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 18².
17. 17.Use a² − b² = (a + b)(a − b) to find 94² − 73².
18. 18.Use (a + b)² = a² + 2ab + b² to find 24².
19. 19.If a + b = 10 and ab = 9, what is a² + b²?
20. 20.If a + b = 10 and ab = 21, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 13².
22. 22.Use (a + b)² = a² + 2ab + b² to find 88².
23. 23.Use a² − b² = (a + b)(a − b) to find 28² − 1².
24. 24.Find the value of x² − y² when x = 5 and y = 4.
25. 25.Use (a + b)(a − b) = a² − b² to find 86 × 74.
26. 26.Find the value of x² − y² when x = 14 and y = 11.
27. 27.Use a² − b² = (a + b)(a − b) to find 34² − 5².
28. 28.Use (a + b)(a − b) = a² − b² to find 52 × 48.
29. 29.Use (a + b)(a − b) = a² − b² to find 23 × 17.
30. 30.Use (a + b)² = a² + 2ab + b² to find 92².
31. 31.Use (a + b)² = a² + 2ab + b² to find 71².
32. 32.Use (a − b)² = a² − 2ab + b² to find 77².
33. 33.Find the value of x² + 2xy + y² when x = 10 and y = 9.
34. 34.If a + b = 6 and ab = 5, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 32².
36. 36.Find the value of x² − 2xy + y² when x = 13 and y = 8.
37. 37.Use (a − b)² = a² − 2ab + b² to find 84².
38. 38.Find the value of x² − y² when x = 3 and y = 2.
39. 39.Use (a + b)² = a² + 2ab + b² to find 51².
40. 40.Find the value of x² − 2xy + y² when x = 11 and y = 5.

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