Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 115 · 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 44².
2. 2.Find the value of x² − y² when x = 4 and y = 2.
3. 3.Use (a − b)² = a² − 2ab + b² to find 11².
4. 4.If a + b = 10 and ab = 21, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 13 and y = 4.
6. 6.Use (a + b)(a − b) = a² − b² to find 78 × 62.
7. 7.Use a² − b² = (a + b)(a − b) to find 48² − 41².
8. 8.Use (a − b)² = a² − 2ab + b² to find 42².
9. 9.If a + b = 3 and ab = 2, what is a² + b²?
10. 10.If a + b = 13 and ab = 22, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 77².
12. 12.Use (a + b)² = a² + 2ab + b² to find 38².
13. 13.Use a² − b² = (a + b)(a − b) to find 80² − 24².
14. 14.If a + b = 8 and ab = 7, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 27² − 10².
16. 16.Use a² − b² = (a + b)(a − b) to find 38² − 19².
17. 17.Find the value of x² − 2xy + y² when x = 12 and y = 9.
18. 18.Use (a + b)² = a² + 2ab + b² to find 101².
19. 19.Use (a + b)(a − b) = a² − b² to find 68 × 52.
20. 20.Use (a + b)² = a² + 2ab + b² to find 47².
21. 21.If a + b = 15 and ab = 54, what is a² + b²?
22. 22.If a + b = 21 and ab = 108, what is a² + b²?
23. 23.Find the value of x² − 2xy + y² when x = 10 and y = 6.
24. 24.Use (a − b)² = a² − 2ab + b² to find 21².
25. 25.Find the value of x² − y² when x = 6 and y = 2.
26. 26.Use (a + b)² = a² + 2ab + b² to find 56².
27. 27.Find the value of x² + 2xy + y² when x = 15 and y = 10.
28. 28.Use (a − b)² = a² − 2ab + b² to find 55².
29. 29.Use (a + b)² = a² + 2ab + b² to find 34².
30. 30.Use (a + b)(a − b) = a² − b² to find 45 × 35.
31. 31.Use (a + b)² = a² + 2ab + b² to find 92².
32. 32.If a + b = 13 and ab = 42, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 26².
34. 34.Use (a + b)(a − b) = a² − b² to find 61 × 59.
35. 35.Use (a + b)² = a² + 2ab + b² to find 29².
36. 36.Use (a + b)² = a² + 2ab + b² to find 27².
37. 37.Find the value of x² − 2xy + y² when x = 8 and y = 6.
38. 38.Use (a + b)(a − b) = a² − b² to find 109 × 91.
39. 39.Use a² − b² = (a + b)(a − b) to find 87² − 50².
40. 40.Use (a + b)² = a² + 2ab + b² to find 35².

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