Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 482 · 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 42 × 38.
2. 2.Use (a + b)(a − b) = a² − b² to find 66 × 54.
3. 3.Use (a + b)² = a² + 2ab + b² to find 79².
4. 4.Use a² − b² = (a + b)(a − b) to find 82² − 32².
5. 5.Use (a + b)² = a² + 2ab + b² to find 37².
6. 6.Use (a − b)² = a² − 2ab + b² to find 98².
7. 7.Use (a + b)² = a² + 2ab + b² to find 51².
8. 8.Find the value of x² − 2xy + y² when x = 13 and y = 8.
9. 9.If a + b = 12 and ab = 11, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 16².
11. 11.Use (a + b)² = a² + 2ab + b² to find 109².
12. 12.Use a² − b² = (a + b)(a − b) to find 58² − 50².
13. 13.Find the value of x² − y² when x = 12 and y = 9.
14. 14.Find the value of x² − y² when x = 4 and y = 3.
15. 15.Use (a + b)(a − b) = a² − b² to find 98 × 82.
16. 16.Use (a − b)² = a² − 2ab + b² to find 33².
17. 17.Find the value of x² + 2xy + y² when x = 10 and y = 7.
18. 18.Use (a + b)² = a² + 2ab + b² to find 101².
19. 19.Use (a + b)(a − b) = a² − b² to find 105 × 95.
20. 20.Find the value of x² − y² when x = 12 and y = 5.
21. 21.Use a² − b² = (a + b)(a − b) to find 84² − 59².
22. 22.Find the value of x² + 2xy + y² when x = 6 and y = 3.
23. 23.Use a² − b² = (a + b)(a − b) to find 78² − 5².
24. 24.If a + b = 19 and ab = 90, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 21².
26. 26.Find the value of x² − y² when x = 12 and y = 8.
27. 27.Use (a − b)² = a² − 2ab + b² to find 87².
28. 28.Find the value of x² + 2xy + y² when x = 12 and y = 10.
29. 29.Use a² − b² = (a + b)(a − b) to find 42² − 11².
30. 30.Use (a + b)² = a² + 2ab + b² to find 26².
31. 31.Use (a − b)² = a² − 2ab + b² to find 47².
32. 32.If a + b = 15 and ab = 36, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 75².
34. 34.Use (a + b)(a − b) = a² − b² to find 77 × 63.
35. 35.Find the value of x² − 2xy + y² when x = 12 and y = 8.
36. 36.Use (a + b)(a − b) = a² − b² to find 88 × 72.
37. 37.Use (a + b)² = a² + 2ab + b² to find 72².
38. 38.Find the value of x² − 2xy + y² when x = 12 and y = 11.
39. 39.If a + b = 17 and ab = 66, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 29² − 18².

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