Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 740 · 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 94² − 45².
2. 2.If a + b = 8 and ab = 15, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 78² − 42².
4. 4.Find the value of x² − y² when x = 9 and y = 3.
5. 5.Use (a + b)(a − b) = a² − b² to find 22 × 18.
6. 6.Use (a + b)² = a² + 2ab + b² to find 22².
7. 7.Find the value of x² + 2xy + y² when x = 5 and y = 4.
8. 8.Find the value of x² + 2xy + y² when x = 13 and y = 3.
9. 9.Use (a − b)² = a² − 2ab + b² to find 94².
10. 10.If a − b = 5 and ab = 66, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 57².
12. 12.Use (a + b)² = a² + 2ab + b² to find 27².
13. 13.Use (a − b)² = a² − 2ab + b² to find 92².
14. 14.Use (a + b)² = a² + 2ab + b² to find 107².
15. 15.Use (a + b)(a − b) = a² − b² to find 58 × 42.
16. 16.Use a² − b² = (a + b)(a − b) to find 44² − 27².
17. 17.If a − b = 4 and ab = 77, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 40² − 33².
19. 19.Find the value of x² + 2xy + y² when x = 4 and y = 1.
20. 20.Find the value of x² − y² when x = 13 and y = 5.
21. 21.If a + b = 15 and ab = 50, what is a² + b²?
22. 22.Find the value of x² − y² when x = 4 and y = 1.
23. 23.If a + b = 11 and ab = 30, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 81 × 79.
25. 25.Use (a + b)² = a² + 2ab + b² to find 56².
26. 26.Use (a + b)² = a² + 2ab + b² to find 19².
27. 27.If a − b = 1 and ab = 2, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 88².
29. 29.Use a² − b² = (a + b)(a − b) to find 66² − 13².
30. 30.Use (a + b)² = a² + 2ab + b² to find 74².
31. 31.Use (a − b)² = a² − 2ab + b² to find 49².
32. 32.Find the value of x² − 2xy + y² when x = 12 and y = 8.
33. 33.Use a² − b² = (a + b)(a − b) to find 83² − 35².
34. 34.Use (a − b)² = a² − 2ab + b² to find 64².
35. 35.Use a² − b² = (a + b)(a − b) to find 71² − 36².
36. 36.If a − b = 3 and ab = 18, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 35².
38. 38.If a − b = 2 and ab = 24, what is a² + b²?
39. 39.If a + b = 5 and ab = 4, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 21 × 19.

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