Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 818 · 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.If a + b = 16 and ab = 60, what is a² + b²?
2. 2.Find the value of x² − y² when x = 6 and y = 2.
3. 3.Find the value of x² + 2xy + y² when x = 8 and y = 2.
4. 4.Use (a + b)² = a² + 2ab + b² to find 62².
5. 5.Find the value of x² + 2xy + y² when x = 7 and y = 5.
6. 6.If a + b = 12 and ab = 32, what is a² + b²?
7. 7.Find the value of x² + 2xy + y² when x = 3 and y = 2.
8. 8.Use (a + b)(a − b) = a² − b² to find 73 × 67.
9. 9.Use (a + b)² = a² + 2ab + b² to find 73².
10. 10.Use (a + b)(a − b) = a² − b² to find 71 × 69.
11. 11.Use (a + b)² = a² + 2ab + b² to find 34².
12. 12.If a − b = 3 and ab = 4, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 44 × 36.
14. 14.Use (a − b)² = a² − 2ab + b² to find 28².
15. 15.Use (a + b)² = a² + 2ab + b² to find 84².
16. 16.Use (a − b)² = a² − 2ab + b² to find 24².
17. 17.Find the value of x² + 2xy + y² when x = 12 and y = 4.
18. 18.Use (a + b)² = a² + 2ab + b² to find 91².
19. 19.Use a² − b² = (a + b)(a − b) to find 42² − 16².
20. 20.Use (a + b)² = a² + 2ab + b² to find 77².
21. 21.If a + b = 4 and ab = 3, what is a² + b²?
22. 22.If a + b = 6 and ab = 8, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 37².
24. 24.Use (a + b)² = a² + 2ab + b² to find 31².
25. 25.If a − b = 7 and ab = 30, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 22 × 18.
27. 27.Use (a + b)² = a² + 2ab + b² to find 78².
28. 28.Find the value of x² − y² when x = 5 and y = 1.
29. 29.If a + b = 22 and ab = 120, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 38 × 22.
31. 31.If a − b = 4 and ab = 21, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 37² − 15².
33. 33.Use (a − b)² = a² − 2ab + b² to find 75².
34. 34.If a − b = 9 and ab = 10, what is a² + b²?
35. 35.Find the value of x² + 2xy + y² when x = 12 and y = 3.
36. 36.Use a² − b² = (a + b)(a − b) to find 20² − 7².
37. 37.Find the value of x² + 2xy + y² when x = 14 and y = 11.
38. 38.Use (a + b)(a − b) = a² − b² to find 39 × 21.
39. 39.Use a² − b² = (a + b)(a − b) to find 95² − 12².
40. 40.If a + b = 14 and ab = 24, what is a² + b²?

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