Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 771 · 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)² = a² + 2ab + b² to find 46².
2. 2.Use (a − b)² = a² − 2ab + b² to find 23².
3. 3.Find the value of x² − y² when x = 9 and y = 1.
4. 4.If a + b = 3 and ab = 2, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 62².
6. 6.Use (a + b)(a − b) = a² − b² to find 32 × 28.
7. 7.Use a² − b² = (a + b)(a − b) to find 68² − 53².
8. 8.Use (a − b)² = a² − 2ab + b² to find 35².
9. 9.Use (a + b)² = a² + 2ab + b² to find 61².
10. 10.If a − b = 4 and ab = 5, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 29².
12. 12.Use (a + b)² = a² + 2ab + b² to find 11².
13. 13.Find the value of x² + 2xy + y² when x = 9 and y = 8.
14. 14.Use (a − b)² = a² − 2ab + b² to find 95².
15. 15.Find the value of x² + 2xy + y² when x = 5 and y = 4.
16. 16.Use (a + b)(a − b) = a² − b² to find 25 × 15.
17. 17.Use (a + b)(a − b) = a² − b² to find 98 × 82.
18. 18.Use (a + b)(a − b) = a² − b² to find 43 × 37.
19. 19.Find the value of x² − y² when x = 3 and y = 1.
20. 20.Use (a + b)(a − b) = a² − b² to find 68 × 52.
21. 21.Use (a − b)² = a² − 2ab + b² to find 92².
22. 22.Use (a − b)² = a² − 2ab + b² to find 54².
23. 23.If a − b = 2 and ab = 48, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 33² − 29².
25. 25.Use (a + b)(a − b) = a² − b² to find 86 × 74.
26. 26.Find the value of x² + 2xy + y² when x = 3 and y = 1.
27. 27.If a − b = 6 and ab = 55, what is a² + b²?
28. 28.If a + b = 14 and ab = 48, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 64².
30. 30.Use (a + b)² = a² + 2ab + b² to find 77².
31. 31.Use (a + b)² = a² + 2ab + b² to find 87².
32. 32.Use (a + b)² = a² + 2ab + b² to find 34².
33. 33.Find the value of x² − y² when x = 15 and y = 5.
34. 34.Use a² − b² = (a + b)(a − b) to find 30² − 3².
35. 35.Use (a + b)(a − b) = a² − b² to find 71 × 69.
36. 36.Find the value of x² − y² when x = 7 and y = 4.
37. 37.Use (a + b)(a − b) = a² − b² to find 59 × 41.
38. 38.Use a² − b² = (a + b)(a − b) to find 51² − 19².
39. 39.Find the value of x² + 2xy + y² when x = 13 and y = 4.
40. 40.Use a² − b² = (a + b)(a − b) to find 65² − 21².

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