Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 41 · 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 42² − 35².
2. 2.Use (a + b)² = a² + 2ab + b² to find 49².
3. 3.Find the value of x² − y² when x = 4 and y = 1.
4. 4.Use (a − b)² = a² − 2ab + b² to find 43².
5. 5.Use (a + b)(a − b) = a² − b² to find 103 × 97.
6. 6.Use (a − b)² = a² − 2ab + b² to find 54².
7. 7.Find the value of x² + 2xy + y² when x = 9 and y = 3.
8. 8.Use a² − b² = (a + b)(a − b) to find 35² − 32².
9. 9.Find the value of x² + 2xy + y² when x = 13 and y = 1.
10. 10.Use (a − b)² = a² − 2ab + b² to find 32².
11. 11.Use (a − b)² = a² − 2ab + b² to find 98².
12. 12.Use (a − b)² = a² − 2ab + b² to find 84².
13. 13.If a + b = 5 and ab = 4, what is a² + b²?
14. 14.Find the value of x² + 2xy + y² when x = 15 and y = 12.
15. 15.If a + b = 3 and ab = 2, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 43 × 37.
17. 17.Use (a + b)(a − b) = a² − b² to find 95 × 85.
18. 18.If a − b = 3 and ab = 4, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 94².
20. 20.If a + b = 4 and ab = 3, what is a² + b²?
21. 21.If a + b = 12 and ab = 35, what is a² + b²?
22. 22.If a − b = 3 and ab = 10, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 77².
24. 24.Use (a − b)² = a² − 2ab + b² to find 85².
25. 25.Use (a + b)(a − b) = a² − b² to find 52 × 48.
26. 26.Use (a + b)(a − b) = a² − b² to find 33 × 27.
27. 27.Use (a + b)(a − b) = a² − b² to find 24 × 16.
28. 28.Use (a − b)² = a² − 2ab + b² to find 25².
29. 29.Use a² − b² = (a + b)(a − b) to find 38² − 4².
30. 30.Use (a − b)² = a² − 2ab + b² to find 21².
31. 31.Use (a + b)² = a² + 2ab + b² to find 52².
32. 32.Use (a + b)² = a² + 2ab + b² to find 38².
33. 33.Find the value of x² − y² when x = 5 and y = 1.
34. 34.Use a² − b² = (a + b)(a − b) to find 53² − 36².
35. 35.If a + b = 15 and ab = 50, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 26².
37. 37.Use a² − b² = (a + b)(a − b) to find 23² − 22².
38. 38.Find the value of x² − y² when x = 6 and y = 5.
39. 39.Find the value of x² + 2xy + y² when x = 6 and y = 4.
40. 40.Use (a + b)² = a² + 2ab + b² to find 92².

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