Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 912 · 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 93².
2. 2.Use (a + b)(a − b) = a² − b² to find 41 × 39.
3. 3.Use (a + b)² = a² + 2ab + b² to find 82².
4. 4.Use (a − b)² = a² − 2ab + b² to find 57².
5. 5.Find the value of x² − y² when x = 3 and y = 1.
6. 6.Use (a + b)² = a² + 2ab + b² to find 21².
7. 7.Find the value of x² − 2xy + y² when x = 4 and y = 3.
8. 8.If a + b = 13 and ab = 22, what is a² + b²?
9. 9.If a + b = 10 and ab = 21, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 38².
11. 11.Use (a + b)² = a² + 2ab + b² to find 85².
12. 12.Use (a − b)² = a² − 2ab + b² to find 73².
13. 13.Use (a − b)² = a² − 2ab + b² to find 14².
14. 14.Use (a − b)² = a² − 2ab + b² to find 29².
15. 15.Find the value of x² + 2xy + y² when x = 10 and y = 2.
16. 16.Use a² − b² = (a + b)(a − b) to find 84² − 65².
17. 17.If a − b = 2 and ab = 8, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 88 × 72.
19. 19.If a + b = 21 and ab = 108, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 36².
21. 21.If a + b = 3 and ab = 2, what is a² + b²?
22. 22.Find the value of x² − 2xy + y² when x = 3 and y = 2.
23. 23.Use (a + b)² = a² + 2ab + b² to find 89².
24. 24.Find the value of x² + 2xy + y² when x = 5 and y = 4.
25. 25.Find the value of x² − y² when x = 13 and y = 7.
26. 26.Use (a + b)(a − b) = a² − b² to find 92 × 88.
27. 27.Use (a + b)(a − b) = a² − b² to find 44 × 36.
28. 28.Find the value of x² − y² when x = 4 and y = 2.
29. 29.Use (a − b)² = a² − 2ab + b² to find 46².
30. 30.Use (a + b)(a − b) = a² − b² to find 105 × 95.
31. 31.If a − b = 6 and ab = 16, what is a² + b²?
32. 32.Find the value of x² + 2xy + y² when x = 9 and y = 5.
33. 33.Use (a + b)² = a² + 2ab + b² to find 18².
34. 34.Use a² − b² = (a + b)(a − b) to find 29² − 20².
35. 35.Use (a + b)² = a² + 2ab + b² to find 37².
36. 36.Use (a + b)² = a² + 2ab + b² to find 109².
37. 37.Use (a + b)(a − b) = a² − b² to find 76 × 64.
38. 38.Use (a + b)(a − b) = a² − b² to find 39 × 21.
39. 39.If a + b = 17 and ab = 72, what is a² + b²?
40. 40.If a − b = 4 and ab = 5, what is a² + b²?

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