Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 832 · 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 71².
2. 2.Find the value of x² − y² when x = 8 and y = 2.
3. 3.If a − b = 1 and ab = 132, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 31² − 21².
5. 5.If a + b = 3 and ab = 2, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 88 × 72.
7. 7.Use (a + b)² = a² + 2ab + b² to find 23².
8. 8.If a − b = 2 and ab = 8, what is a² + b²?
9. 9.If a + b = 9 and ab = 14, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 27².
11. 11.Use (a + b)(a − b) = a² − b² to find 23 × 17.
12. 12.Find the value of x² + 2xy + y² when x = 11 and y = 1.
13. 13.Find the value of x² + 2xy + y² when x = 14 and y = 7.
14. 14.Use (a + b)² = a² + 2ab + b² to find 25².
15. 15.Find the value of x² − y² when x = 11 and y = 8.
16. 16.If a + b = 13 and ab = 22, what is a² + b²?
17. 17.If a + b = 5 and ab = 6, what is a² + b²?
18. 18.If a + b = 13 and ab = 12, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 95².
20. 20.Use (a + b)(a − b) = a² − b² to find 41 × 39.
21. 21.Find the value of x² − y² when x = 10 and y = 3.
22. 22.If a + b = 12 and ab = 11, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 43 × 37.
24. 24.Use (a + b)(a − b) = a² − b² to find 65 × 55.
25. 25.Use (a + b)(a − b) = a² − b² to find 29 × 11.
26. 26.Use a² − b² = (a + b)(a − b) to find 40² − 1².
27. 27.Use (a + b)² = a² + 2ab + b² to find 34².
28. 28.Find the value of x² − 2xy + y² when x = 11 and y = 6.
29. 29.Use (a − b)² = a² − 2ab + b² to find 32².
30. 30.Use (a + b)² = a² + 2ab + b² to find 55².
31. 31.Find the value of x² − 2xy + y² when x = 6 and y = 5.
32. 32.Use (a + b)² = a² + 2ab + b² to find 84².
33. 33.Use (a + b)(a − b) = a² − b² to find 54 × 46.
34. 34.Use a² − b² = (a + b)(a − b) to find 58² − 56².
35. 35.Use (a − b)² = a² − 2ab + b² to find 87².
36. 36.If a − b = 1 and ab = 2, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 88².
38. 38.Find the value of x² − 2xy + y² when x = 14 and y = 9.
39. 39.Use (a − b)² = a² − 2ab + b² to find 84².
40. 40.If a + b = 16 and ab = 60, what is a² + b²?

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