Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 244 · 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 52².
2. 2.Use (a + b)(a − b) = a² − b² to find 91 × 89.
3. 3.If a − b = 6 and ab = 27, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 79² − 78².
5. 5.Find the value of x² + 2xy + y² when x = 5 and y = 2.
6. 6.Find the value of x² − y² when x = 3 and y = 2.
7. 7.Find the value of x² + 2xy + y² when x = 12 and y = 2.
8. 8.Use (a − b)² = a² − 2ab + b² to find 97².
9. 9.Use (a − b)² = a² − 2ab + b² to find 15².
10. 10.If a + b = 14 and ab = 48, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 11².
12. 12.Use (a + b)² = a² + 2ab + b² to find 26².
13. 13.Use (a − b)² = a² − 2ab + b² to find 11².
14. 14.If a − b = 8 and ab = 20, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 12².
16. 16.If a + b = 12 and ab = 20, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 73² − 12².
18. 18.Use (a − b)² = a² − 2ab + b² to find 54².
19. 19.Find the value of x² + 2xy + y² when x = 5 and y = 1.
20. 20.Use (a + b)² = a² + 2ab + b² to find 16².
21. 21.Use a² − b² = (a + b)(a − b) to find 64² − 28².
22. 22.Use (a + b)(a − b) = a² − b² to find 109 × 91.
23. 23.Use (a + b)² = a² + 2ab + b² to find 38².
24. 24.Use (a + b)(a − b) = a² − b² to find 47 × 33.
25. 25.Use a² − b² = (a + b)(a − b) to find 82² − 5².
26. 26.Use (a + b)² = a² + 2ab + b² to find 18².
27. 27.If a + b = 6 and ab = 8, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 22 × 18.
29. 29.Use a² − b² = (a + b)(a − b) to find 69² − 65².
30. 30.Find the value of x² + 2xy + y² when x = 3 and y = 1.
31. 31.Use (a + b)² = a² + 2ab + b² to find 73².
32. 32.If a − b = 6 and ab = 55, what is a² + b²?
33. 33.If a + b = 17 and ab = 60, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 94².
35. 35.Use a² − b² = (a + b)(a − b) to find 37² − 28².
36. 36.If a + b = 19 and ab = 90, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 87².
38. 38.Use (a + b)² = a² + 2ab + b² to find 99².
39. 39.Find the value of x² + 2xy + y² when x = 15 and y = 7.
40. 40.If a + b = 4 and ab = 3, what is a² + b²?

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