Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 23 · 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 = 1 and ab = 6, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 47².
3. 3.Use (a + b)² = a² + 2ab + b² to find 38².
4. 4.If a − b = 4 and ab = 32, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 74².
6. 6.If a − b = 6 and ab = 16, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 55² − 14².
8. 8.Use (a + b)(a − b) = a² − b² to find 36 × 24.
9. 9.Use (a − b)² = a² − 2ab + b² to find 31².
10. 10.Use (a + b)(a − b) = a² − b² to find 75 × 65.
11. 11.Use (a + b)² = a² + 2ab + b² to find 31².
12. 12.If a − b = 2 and ab = 48, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 106².
14. 14.Use a² − b² = (a + b)(a − b) to find 47² − 44².
15. 15.Use (a + b)² = a² + 2ab + b² to find 74².
16. 16.Use (a + b)(a − b) = a² − b² to find 81 × 79.
17. 17.If a − b = 5 and ab = 50, what is a² + b²?
18. 18.If a + b = 13 and ab = 36, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 68².
20. 20.Use (a + b)² = a² + 2ab + b² to find 88².
21. 21.Use (a + b)² = a² + 2ab + b² to find 57².
22. 22.Use (a + b)(a − b) = a² − b² to find 27 × 13.
23. 23.Find the value of x² + 2xy + y² when x = 10 and y = 9.
24. 24.Find the value of x² − 2xy + y² when x = 6 and y = 1.
25. 25.Use a² − b² = (a + b)(a − b) to find 20² − 7².
26. 26.Find the value of x² − 2xy + y² when x = 6 and y = 2.
27. 27.Use a² − b² = (a + b)(a − b) to find 55² − 23².
28. 28.If a + b = 7 and ab = 10, what is a² + b²?
29. 29.Find the value of x² − y² when x = 7 and y = 6.
30. 30.If a + b = 3 and ab = 2, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 34 × 26.
32. 32.If a − b = 5 and ab = 6, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 19².
34. 34.If a + b = 17 and ab = 72, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 48 × 32.
36. 36.Find the value of x² − 2xy + y² when x = 4 and y = 1.
37. 37.Use (a + b)² = a² + 2ab + b² to find 102².
38. 38.Use (a − b)² = a² − 2ab + b² to find 99².
39. 39.Use a² − b² = (a + b)(a − b) to find 57² − 35².
40. 40.Use (a + b)(a − b) = a² − b² to find 87 × 73.

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