Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 806 · 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 = 11 and ab = 18, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 69².
3. 3.Use (a + b)² = a² + 2ab + b² to find 27².
4. 4.Find the value of x² − 2xy + y² when x = 3 and y = 2.
5. 5.Use (a + b)² = a² + 2ab + b² to find 101².
6. 6.Use (a − b)² = a² − 2ab + b² to find 58².
7. 7.If a − b = 2 and ab = 8, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 85².
9. 9.Use (a − b)² = a² − 2ab + b² to find 31².
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 96².
12. 12.Use (a − b)² = a² − 2ab + b² to find 23².
13. 13.Use (a + b)² = a² + 2ab + b² to find 19².
14. 14.Find the value of x² − y² when x = 5 and y = 1.
15. 15.Use a² − b² = (a + b)(a − b) to find 80² − 62².
16. 16.Use (a + b)² = a² + 2ab + b² to find 24².
17. 17.Use (a − b)² = a² − 2ab + b² to find 34².
18. 18.Use (a − b)² = a² − 2ab + b² to find 99².
19. 19.Use (a + b)(a − b) = a² − b² to find 42 × 38.
20. 20.Find the value of x² − 2xy + y² when x = 10 and y = 6.
21. 21.Find the value of x² − y² when x = 3 and y = 2.
22. 22.If a − b = 3 and ab = 54, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 39².
24. 24.Use (a + b)(a − b) = a² − b² to find 21 × 19.
25. 25.If a + b = 11 and ab = 24, what is a² + b²?
26. 26.If a − b = 1 and ab = 2, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 72².
28. 28.Use (a + b)(a − b) = a² − b² to find 26 × 14.
29. 29.Use (a + b)(a − b) = a² − b² to find 109 × 91.
30. 30.If a + b = 8 and ab = 12, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 16².
32. 32.Use a² − b² = (a + b)(a − b) to find 43² − 32².
33. 33.Find the value of x² + 2xy + y² when x = 6 and y = 5.
34. 34.Use (a + b)² = a² + 2ab + b² to find 48².
35. 35.Use (a + b)² = a² + 2ab + b² to find 82².
36. 36.Use (a − b)² = a² − 2ab + b² to find 67².
37. 37.Use (a + b)² = a² + 2ab + b² to find 44².
38. 38.Use (a + b)(a − b) = a² − b² to find 47 × 33.
39. 39.Find the value of x² − y² when x = 7 and y = 5.
40. 40.Use a² − b² = (a + b)(a − b) to find 42² − 37².

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