Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 118 · 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 55 × 45.
2. 2.Find the value of x² − y² when x = 13 and y = 10.
3. 3.Find the value of x² + 2xy + y² when x = 5 and y = 1.
4. 4.Use a² − b² = (a + b)(a − b) to find 83² − 5².
5. 5.Find the value of x² − y² when x = 11 and y = 8.
6. 6.Use (a + b)² = a² + 2ab + b² to find 32².
7. 7.Use (a − b)² = a² − 2ab + b² to find 91².
8. 8.Use (a − b)² = a² − 2ab + b² to find 38².
9. 9.Use a² − b² = (a + b)(a − b) to find 83² − 64².
10. 10.Use a² − b² = (a + b)(a − b) to find 58² − 13².
11. 11.Use (a − b)² = a² − 2ab + b² to find 86².
12. 12.Use (a − b)² = a² − 2ab + b² to find 93².
13. 13.If a − b = 9 and ab = 10, what is a² + b²?
14. 14.Find the value of x² − 2xy + y² when x = 6 and y = 2.
15. 15.Use a² − b² = (a + b)(a − b) to find 26² − 10².
16. 16.Use a² − b² = (a + b)(a − b) to find 31² − 20².
17. 17.Use a² − b² = (a + b)(a − b) to find 99² − 36².
18. 18.Find the value of x² + 2xy + y² when x = 12 and y = 10.
19. 19.Use (a − b)² = a² − 2ab + b² to find 73².
20. 20.Use (a − b)² = a² − 2ab + b² to find 18².
21. 21.Use (a + b)² = a² + 2ab + b² to find 91².
22. 22.Find the value of x² + 2xy + y² when x = 4 and y = 3.
23. 23.Use (a + b)² = a² + 2ab + b² to find 84².
24. 24.Use a² − b² = (a + b)(a − b) to find 95² − 34².
25. 25.Use (a + b)² = a² + 2ab + b² to find 99².
26. 26.If a + b = 7 and ab = 6, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 98².
28. 28.If a + b = 23 and ab = 132, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 84 × 76.
30. 30.Use (a + b)² = a² + 2ab + b² to find 14².
31. 31.Use (a + b)(a − b) = a² − b² to find 88 × 72.
32. 32.Use (a − b)² = a² − 2ab + b² to find 43².
33. 33.Use (a + b)² = a² + 2ab + b² to find 85².
34. 34.Find the value of x² − 2xy + y² when x = 5 and y = 3.
35. 35.Use (a + b)² = a² + 2ab + b² to find 54².
36. 36.Use a² − b² = (a + b)(a − b) to find 84² − 25².
37. 37.Use (a + b)(a − b) = a² − b² to find 47 × 33.
38. 38.Use a² − b² = (a + b)(a − b) to find 32² − 13².
39. 39.Use (a + b)² = a² + 2ab + b² to find 67².
40. 40.Find the value of x² − 2xy + y² when x = 4 and y = 1.

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