Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 822 · 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 = 2 and ab = 15, what is a² + b²?
2. 2.Find the value of x² − 2xy + y² when x = 7 and y = 1.
3. 3.Use (a + b)² = a² + 2ab + b² to find 58².
4. 4.Use (a − b)² = a² − 2ab + b² to find 41².
5. 5.Use a² − b² = (a + b)(a − b) to find 63² − 8².
6. 6.Use a² − b² = (a + b)(a − b) to find 51² − 28².
7. 7.Use (a + b)² = a² + 2ab + b² to find 49².
8. 8.Use (a − b)² = a² − 2ab + b² to find 38².
9. 9.Use (a + b)(a − b) = a² − b² to find 32 × 28.
10. 10.Use (a + b)(a − b) = a² − b² to find 61 × 59.
11. 11.Use (a − b)² = a² − 2ab + b² to find 72².
12. 12.Use (a − b)² = a² − 2ab + b² to find 69².
13. 13.Find the value of x² − y² when x = 8 and y = 3.
14. 14.Use (a − b)² = a² − 2ab + b² to find 65².
15. 15.Use (a + b)(a − b) = a² − b² to find 33 × 27.
16. 16.Use a² − b² = (a + b)(a − b) to find 48² − 36².
17. 17.Use (a + b)(a − b) = a² − b² to find 58 × 42.
18. 18.Use a² − b² = (a + b)(a − b) to find 53² − 41².
19. 19.Use (a + b)² = a² + 2ab + b² to find 102².
20. 20.Use (a + b)(a − b) = a² − b² to find 21 × 19.
21. 21.Use (a + b)² = a² + 2ab + b² to find 29².
22. 22.Use (a − b)² = a² − 2ab + b² to find 25².
23. 23.Use (a + b)² = a² + 2ab + b² to find 93².
24. 24.Find the value of x² − 2xy + y² when x = 9 and y = 1.
25. 25.Use (a − b)² = a² − 2ab + b² to find 45².
26. 26.Use a² − b² = (a + b)(a − b) to find 90² − 46².
27. 27.Use (a + b)² = a² + 2ab + b² to find 74².
28. 28.Use a² − b² = (a + b)(a − b) to find 90² − 63².
29. 29.Find the value of x² − y² when x = 9 and y = 6.
30. 30.Find the value of x² − y² when x = 14 and y = 10.
31. 31.Use (a − b)² = a² − 2ab + b² to find 93².
32. 32.Use a² − b² = (a + b)(a − b) to find 78² − 8².
33. 33.Use a² − b² = (a + b)(a − b) to find 80² − 28².
34. 34.If a − b = 1 and ab = 20, what is a² + b²?
35. 35.If a + b = 6 and ab = 8, what is a² + b²?
36. 36.Find the value of x² + 2xy + y² when x = 11 and y = 1.
37. 37.Find the value of x² − y² when x = 4 and y = 3.
38. 38.Use a² − b² = (a + b)(a − b) to find 55² − 1².
39. 39.Use (a − b)² = a² − 2ab + b² to find 49².
40. 40.Use (a + b)² = a² + 2ab + b² to find 22².

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