Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 303 · 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 59 × 41.
2. 2.If a − b = 1 and ab = 2, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 15².
4. 4.Use a² − b² = (a + b)(a − b) to find 28² − 26².
5. 5.Use (a + b)² = a² + 2ab + b² to find 69².
6. 6.Use a² − b² = (a + b)(a − b) to find 83² − 55².
7. 7.Use (a + b)² = a² + 2ab + b² to find 22².
8. 8.Find the value of x² − 2xy + y² when x = 12 and y = 5.
9. 9.If a − b = 3 and ab = 10, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 43 × 37.
11. 11.If a + b = 5 and ab = 4, what is a² + b²?
12. 12.If a − b = 1 and ab = 6, what is a² + b²?
13. 13.If a + b = 5 and ab = 6, what is a² + b²?
14. 14.If a + b = 12 and ab = 35, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 96 × 84.
16. 16.Find the value of x² + 2xy + y² when x = 14 and y = 2.
17. 17.Use (a + b)² = a² + 2ab + b² to find 58².
18. 18.Find the value of x² − y² when x = 13 and y = 8.
19. 19.Find the value of x² − y² when x = 13 and y = 4.
20. 20.Use (a − b)² = a² − 2ab + b² to find 22².
21. 21.If a − b = 3 and ab = 40, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 52 × 48.
23. 23.Use a² − b² = (a + b)(a − b) to find 25² − 13².
24. 24.Use (a + b)(a − b) = a² − b² to find 34 × 26.
25. 25.Find the value of x² + 2xy + y² when x = 11 and y = 1.
26. 26.Use (a − b)² = a² − 2ab + b² to find 15².
27. 27.Use (a + b)² = a² + 2ab + b² to find 55².
28. 28.Use a² − b² = (a + b)(a − b) to find 81² − 61².
29. 29.Use (a + b)² = a² + 2ab + b² to find 33².
30. 30.Use (a − b)² = a² − 2ab + b² to find 23².
31. 31.Use a² − b² = (a + b)(a − b) to find 33² − 32².
32. 32.Use (a − b)² = a² − 2ab + b² to find 67².
33. 33.Use (a + b)² = a² + 2ab + b² to find 92².
34. 34.Use a² − b² = (a + b)(a − b) to find 25² − 2².
35. 35.Use (a + b)(a − b) = a² − b² to find 31 × 29.
36. 36.Find the value of x² + 2xy + y² when x = 8 and y = 6.
37. 37.Use (a − b)² = a² − 2ab + b² to find 42².
38. 38.Use (a + b)(a − b) = a² − b² to find 24 × 16.
39. 39.Use (a − b)² = a² − 2ab + b² to find 93².
40. 40.Use (a + b)(a − b) = a² − b² to find 42 × 38.

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