Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 713 · 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 16².
2. 2.If a − b = 2 and ab = 8, what is a² + b²?
3. 3.Find the value of x² − y² when x = 11 and y = 6.
4. 4.Use (a + b)² = a² + 2ab + b² to find 43².
5. 5.If a − b = 1 and ab = 72, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 86².
7. 7.Use a² − b² = (a + b)(a − b) to find 40² − 34².
8. 8.Find the value of x² + 2xy + y² when x = 12 and y = 11.
9. 9.Find the value of x² + 2xy + y² when x = 6 and y = 3.
10. 10.Use (a + b)(a − b) = a² − b² to find 49 × 31.
11. 11.Use (a − b)² = a² − 2ab + b² to find 87².
12. 12.Use (a + b)² = a² + 2ab + b² to find 63².
13. 13.Find the value of x² − y² when x = 4 and y = 1.
14. 14.Use a² − b² = (a + b)(a − b) to find 57² − 52².
15. 15.If a − b = 1 and ab = 6, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 92².
17. 17.Find the value of x² − y² when x = 10 and y = 1.
18. 18.Use a² − b² = (a + b)(a − b) to find 40² − 39².
19. 19.Use a² − b² = (a + b)(a − b) to find 87² − 36².
20. 20.Use (a + b)² = a² + 2ab + b² to find 22².
21. 21.Use (a − b)² = a² − 2ab + b² to find 75².
22. 22.Use (a + b)(a − b) = a² − b² to find 95 × 85.
23. 23.Use a² − b² = (a + b)(a − b) to find 39² − 6².
24. 24.Use (a − b)² = a² − 2ab + b² to find 44².
25. 25.Use (a + b)² = a² + 2ab + b² to find 53².
26. 26.Use (a + b)² = a² + 2ab + b² to find 66².
27. 27.Use a² − b² = (a + b)(a − b) to find 71² − 33².
28. 28.Use a² − b² = (a + b)(a − b) to find 70² − 21².
29. 29.Use (a + b)(a − b) = a² − b² to find 38 × 22.
30. 30.Use (a − b)² = a² − 2ab + b² to find 26².
31. 31.Use (a + b)(a − b) = a² − b² to find 37 × 23.
32. 32.Use (a + b)² = a² + 2ab + b² to find 91².
33. 33.If a + b = 19 and ab = 90, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 25².
35. 35.Find the value of x² + 2xy + y² when x = 11 and y = 1.
36. 36.Use (a − b)² = a² − 2ab + b² to find 89².
37. 37.Find the value of x² − 2xy + y² when x = 6 and y = 2.
38. 38.Use (a − b)² = a² − 2ab + b² to find 12².
39. 39.Use a² − b² = (a + b)(a − b) to find 90² − 46².
40. 40.Use (a − b)² = a² − 2ab + b² to find 35².

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