Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 939 · 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.Find the value of x² − y² when x = 9 and y = 6.
2. 2.Use (a − b)² = a² − 2ab + b² to find 19².
3. 3.Find the value of x² − 2xy + y² when x = 10 and y = 4.
4. 4.Use (a + b)(a − b) = a² − b² to find 87 × 73.
5. 5.Use (a + b)² = a² + 2ab + b² to find 97².
6. 6.Use (a + b)² = a² + 2ab + b² to find 33².
7. 7.Use a² − b² = (a + b)(a − b) to find 84² − 54².
8. 8.Use (a + b)² = a² + 2ab + b² to find 16².
9. 9.Use (a + b)(a − b) = a² − b² to find 71 × 69.
10. 10.Use (a + b)² = a² + 2ab + b² to find 37².
11. 11.Use (a + b)² = a² + 2ab + b² to find 21².
12. 12.Use (a + b)(a − b) = a² − b² to find 66 × 54.
13. 13.Use (a − b)² = a² − 2ab + b² to find 59².
14. 14.If a + b = 8 and ab = 15, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 58².
16. 16.Use (a − b)² = a² − 2ab + b² to find 69².
17. 17.Use (a − b)² = a² − 2ab + b² to find 98².
18. 18.Use (a + b)² = a² + 2ab + b² to find 105².
19. 19.Use (a + b)(a − b) = a² − b² to find 88 × 72.
20. 20.If a − b = 2 and ab = 3, what is a² + b²?
21. 21.Find the value of x² − y² when x = 5 and y = 4.
22. 22.Use (a + b)(a − b) = a² − b² to find 43 × 37.
23. 23.Use (a − b)² = a² − 2ab + b² to find 81².
24. 24.Use (a + b)(a − b) = a² − b² to find 108 × 92.
25. 25.Use a² − b² = (a + b)(a − b) to find 89² − 44².
26. 26.Find the value of x² − y² when x = 10 and y = 3.
27. 27.If a − b = 6 and ab = 7, what is a² + b²?
28. 28.Find the value of x² + 2xy + y² when x = 11 and y = 3.
29. 29.Find the value of x² + 2xy + y² when x = 5 and y = 4.
30. 30.Use (a + b)(a − b) = a² − b² to find 69 × 51.
31. 31.Use (a + b)(a − b) = a² − b² to find 61 × 59.
32. 32.Use (a + b)² = a² + 2ab + b² to find 46².
33. 33.Use (a + b)(a − b) = a² − b² to find 82 × 78.
34. 34.Use (a + b)(a − b) = a² − b² to find 109 × 91.
35. 35.Use (a + b)² = a² + 2ab + b² to find 32².
36. 36.If a − b = 4 and ab = 32, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 69².
38. 38.Use (a + b)² = a² + 2ab + b² to find 43².
39. 39.Use a² − b² = (a + b)(a − b) to find 43² − 29².
40. 40.Use (a − b)² = a² − 2ab + b² to find 13².

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