Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 553 · 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 36² − 19².
2. 2.Use (a + b)(a − b) = a² − b² to find 64 × 56.
3. 3.Use (a + b)² = a² + 2ab + b² to find 91².
4. 4.Find the value of x² + 2xy + y² when x = 15 and y = 9.
5. 5.Use (a + b)² = a² + 2ab + b² to find 25².
6. 6.Use (a + b)² = a² + 2ab + b² to find 63².
7. 7.Use (a + b)(a − b) = a² − b² to find 22 × 18.
8. 8.Use a² − b² = (a + b)(a − b) to find 61² − 8².
9. 9.Use (a + b)(a − b) = a² − b² to find 55 × 45.
10. 10.Use (a + b)² = a² + 2ab + b² to find 22².
11. 11.Use (a + b)(a − b) = a² − b² to find 46 × 34.
12. 12.Use (a − b)² = a² − 2ab + b² to find 46².
13. 13.Use a² − b² = (a + b)(a − b) to find 63² − 50².
14. 14.If a − b = 2 and ab = 3, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 62 × 58.
16. 16.Use (a + b)² = a² + 2ab + b² to find 42².
17. 17.Use (a + b)(a − b) = a² − b² to find 82 × 78.
18. 18.Use (a + b)² = a² + 2ab + b² to find 81².
19. 19.Find the value of x² − 2xy + y² when x = 8 and y = 2.
20. 20.Find the value of x² + 2xy + y² when x = 7 and y = 4.
21. 21.Use a² − b² = (a + b)(a − b) to find 33² − 25².
22. 22.Use (a − b)² = a² − 2ab + b² to find 44².
23. 23.Use (a + b)² = a² + 2ab + b² to find 47².
24. 24.If a + b = 6 and ab = 8, what is a² + b²?
25. 25.Find the value of x² − 2xy + y² when x = 14 and y = 8.
26. 26.Find the value of x² − 2xy + y² when x = 5 and y = 1.
27. 27.If a − b = 3 and ab = 40, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 23² − 21².
29. 29.If a − b = 3 and ab = 4, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 72².
31. 31.If a + b = 10 and ab = 9, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 32².
33. 33.Use (a − b)² = a² − 2ab + b² to find 49².
34. 34.Use (a + b)(a − b) = a² − b² to find 26 × 14.
35. 35.Use (a + b)² = a² + 2ab + b² to find 36².
36. 36.Use (a − b)² = a² − 2ab + b² to find 47².
37. 37.Use (a − b)² = a² − 2ab + b² to find 95².
38. 38.Use (a + b)(a − b) = a² − b² to find 42 × 38.
39. 39.Find the value of x² − 2xy + y² when x = 3 and y = 2.
40. 40.Use a² − b² = (a + b)(a − b) to find 86² − 47².

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