Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 922 · 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 51² − 4².
2. 2.Use (a − b)² = a² − 2ab + b² to find 12².
3. 3.Find the value of x² + 2xy + y² when x = 15 and y = 4.
4. 4.Use (a + b)(a − b) = a² − b² to find 24 × 16.
5. 5.Use (a − b)² = a² − 2ab + b² to find 13².
6. 6.If a + b = 3 and ab = 2, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 59² − 28².
8. 8.If a + b = 5 and ab = 6, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 37² − 20².
10. 10.Use (a + b)² = a² + 2ab + b² to find 91².
11. 11.Use (a − b)² = a² − 2ab + b² to find 58².
12. 12.If a − b = 3 and ab = 4, what is a² + b²?
13. 13.If a + b = 20 and ab = 96, what is a² + b²?
14. 14.Find the value of x² − y² when x = 11 and y = 1.
15. 15.Use (a − b)² = a² − 2ab + b² to find 62².
16. 16.Use (a + b)(a − b) = a² − b² to find 22 × 18.
17. 17.Find the value of x² − y² when x = 8 and y = 4.
18. 18.Use (a + b)² = a² + 2ab + b² to find 28².
19. 19.Use (a + b)(a − b) = a² − b² to find 87 × 73.
20. 20.Use (a − b)² = a² − 2ab + b² to find 39².
21. 21.Find the value of x² − 2xy + y² when x = 11 and y = 8.
22. 22.Use a² − b² = (a + b)(a − b) to find 85² − 38².
23. 23.Use (a − b)² = a² − 2ab + b² to find 36².
24. 24.Use (a + b)(a − b) = a² − b² to find 65 × 55.
25. 25.Find the value of x² − y² when x = 9 and y = 3.
26. 26.If a + b = 8 and ab = 7, what is a² + b²?
27. 27.If a − b = 4 and ab = 5, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 31².
29. 29.Use (a − b)² = a² − 2ab + b² to find 28².
30. 30.Use (a + b)² = a² + 2ab + b² to find 65².
31. 31.Use a² − b² = (a + b)(a − b) to find 29² − 10².
32. 32.Find the value of x² + 2xy + y² when x = 12 and y = 9.
33. 33.Use (a + b)(a − b) = a² − b² to find 94 × 86.
34. 34.Use (a + b)(a − b) = a² − b² to find 109 × 91.
35. 35.Use (a + b)(a − b) = a² − b² to find 71 × 69.
36. 36.If a + b = 7 and ab = 10, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 87².
38. 38.Use (a + b)(a − b) = a² − b² to find 43 × 37.
39. 39.Use (a + b)(a − b) = a² − b² to find 45 × 35.
40. 40.Use (a + b)(a − b) = a² − b² to find 102 × 98.

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