Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 440 · 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)(a − b) = a² − b² to find 77 × 63.
2. 2.Use (a + b)² = a² + 2ab + b² to find 31².
3. 3.If a − b = 1 and ab = 6, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 49².
5. 5.Find the value of x² − 2xy + y² when x = 6 and y = 1.
6. 6.If a + b = 4 and ab = 3, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 59 × 41.
8. 8.Use a² − b² = (a + b)(a − b) to find 47² − 3².
9. 9.If a + b = 9 and ab = 20, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 87².
11. 11.Use (a + b)² = a² + 2ab + b² to find 79².
12. 12.Use (a + b)² = a² + 2ab + b² to find 98².
13. 13.Use (a + b)(a − b) = a² − b² to find 108 × 92.
14. 14.Use (a + b)(a − b) = a² − b² to find 49 × 31.
15. 15.Use (a + b)² = a² + 2ab + b² to find 54².
16. 16.If a − b = 2 and ab = 3, what is a² + b²?
17. 17.Find the value of x² − y² when x = 8 and y = 5.
18. 18.Use (a + b)(a − b) = a² − b² to find 106 × 94.
19. 19.Find the value of x² − 2xy + y² when x = 7 and y = 5.
20. 20.Use a² − b² = (a + b)(a − b) to find 55² − 30².
21. 21.Use (a − b)² = a² − 2ab + b² to find 98².
22. 22.Use (a + b)(a − b) = a² − b² to find 72 × 68.
23. 23.Use a² − b² = (a + b)(a − b) to find 47² − 6².
24. 24.Use (a − b)² = a² − 2ab + b² to find 69².
25. 25.Use a² − b² = (a + b)(a − b) to find 22² − 19².
26. 26.Use (a + b)² = a² + 2ab + b² to find 67².
27. 27.Use (a + b)(a − b) = a² − b² to find 97 × 83.
28. 28.Use (a − b)² = a² − 2ab + b² to find 59².
29. 29.Use a² − b² = (a + b)(a − b) to find 57² − 38².
30. 30.Use (a − b)² = a² − 2ab + b² to find 49².
31. 31.Use a² − b² = (a + b)(a − b) to find 27² − 8².
32. 32.Use a² − b² = (a + b)(a − b) to find 77² − 50².
33. 33.Find the value of x² − 2xy + y² when x = 7 and y = 6.
34. 34.Use (a + b)(a − b) = a² − b² to find 57 × 43.
35. 35.Find the value of x² − y² when x = 15 and y = 2.
36. 36.Find the value of x² − y² when x = 5 and y = 1.
37. 37.Use (a + b)(a − b) = a² − b² to find 94 × 86.
38. 38.Use (a + b)² = a² + 2ab + b² to find 17².
39. 39.Use (a + b)² = a² + 2ab + b² to find 28².
40. 40.Use a² − b² = (a + b)(a − b) to find 23² − 21².

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