Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 234 · 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)² = a² + 2ab + b² to find 48².
2. 2.Use (a + b)² = a² + 2ab + b² to find 21².
3. 3.Use (a + b)² = a² + 2ab + b² to find 92².
4. 4.Find the value of x² − y² when x = 7 and y = 2.
5. 5.Find the value of x² + 2xy + y² when x = 5 and y = 1.
6. 6.Use (a + b)² = a² + 2ab + b² to find 19².
7. 7.If a − b = 3 and ab = 18, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 45² − 36².
9. 9.Use (a + b)(a − b) = a² − b² to find 99 × 81.
10. 10.If a − b = 2 and ab = 35, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 101².
12. 12.Use (a − b)² = a² − 2ab + b² to find 22².
13. 13.If a + b = 9 and ab = 14, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 93² − 75².
15. 15.Use a² − b² = (a + b)(a − b) to find 42² − 21².
16. 16.Use a² − b² = (a + b)(a − b) to find 48² − 26².
17. 17.Use (a + b)² = a² + 2ab + b² to find 51².
18. 18.Use (a + b)(a − b) = a² − b² to find 26 × 14.
19. 19.Find the value of x² − 2xy + y² when x = 4 and y = 1.
20. 20.Use (a − b)² = a² − 2ab + b² to find 78².
21. 21.Use a² − b² = (a + b)(a − b) to find 74² − 23².
22. 22.Use a² − b² = (a + b)(a − b) to find 87² − 20².
23. 23.Use (a + b)² = a² + 2ab + b² to find 96².
24. 24.Find the value of x² − y² when x = 8 and y = 4.
25. 25.Use a² − b² = (a + b)(a − b) to find 30² − 29².
26. 26.Use (a + b)² = a² + 2ab + b² to find 29².
27. 27.Use (a + b)(a − b) = a² − b² to find 56 × 44.
28. 28.Use a² − b² = (a + b)(a − b) to find 93² − 42².
29. 29.Find the value of x² − y² when x = 6 and y = 2.
30. 30.Find the value of x² − y² when x = 3 and y = 2.
31. 31.If a − b = 3 and ab = 28, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 28 × 12.
33. 33.If a + b = 10 and ab = 9, what is a² + b²?
34. 34.Find the value of x² + 2xy + y² when x = 4 and y = 2.
35. 35.Use (a − b)² = a² − 2ab + b² to find 39².
36. 36.Use a² − b² = (a + b)(a − b) to find 63² − 16².
37. 37.Find the value of x² + 2xy + y² when x = 13 and y = 12.
38. 38.Use (a + b)² = a² + 2ab + b² to find 25².
39. 39.Use a² − b² = (a + b)(a − b) to find 94² − 21².
40. 40.Use (a + b)² = a² + 2ab + b² to find 24².

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