Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 123 · 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 81².
2. 2.If a + b = 17 and ab = 72, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 75².
4. 4.If a + b = 16 and ab = 60, what is a² + b²?
5. 5.Find the value of x² + 2xy + y² when x = 6 and y = 2.
6. 6.Find the value of x² + 2xy + y² when x = 10 and y = 3.
7. 7.Use (a + b)² = a² + 2ab + b² to find 79².
8. 8.Use (a − b)² = a² − 2ab + b² to find 32².
9. 9.Use a² − b² = (a + b)(a − b) to find 54² − 19².
10. 10.Use (a + b)² = a² + 2ab + b² to find 99².
11. 11.Use (a − b)² = a² − 2ab + b² to find 48².
12. 12.Use (a − b)² = a² − 2ab + b² to find 16².
13. 13.Use (a − b)² = a² − 2ab + b² to find 24².
14. 14.Use (a + b)(a − b) = a² − b² to find 41 × 39.
15. 15.Use (a + b)² = a² + 2ab + b² to find 77².
16. 16.Use (a + b)(a − b) = a² − b² to find 22 × 18.
17. 17.Find the value of x² − y² when x = 3 and y = 2.
18. 18.Use (a − b)² = a² − 2ab + b² to find 59².
19. 19.Use (a + b)(a − b) = a² − b² to find 73 × 67.
20. 20.Use (a − b)² = a² − 2ab + b² to find 43².
21. 21.Use a² − b² = (a + b)(a − b) to find 70² − 20².
22. 22.Use (a + b)² = a² + 2ab + b² to find 46².
23. 23.Use (a + b)² = a² + 2ab + b² to find 43².
24. 24.Use (a + b)² = a² + 2ab + b² to find 26².
25. 25.Use (a + b)(a − b) = a² − b² to find 34 × 26.
26. 26.Use (a + b)(a − b) = a² − b² to find 46 × 34.
27. 27.Use (a + b)² = a² + 2ab + b² to find 81².
28. 28.If a + b = 9 and ab = 20, what is a² + b²?
29. 29.Find the value of x² − y² when x = 4 and y = 1.
30. 30.Use (a − b)² = a² − 2ab + b² to find 93².
31. 31.If a + b = 3 and ab = 2, what is a² + b²?
32. 32.If a + b = 12 and ab = 32, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 25² − 1².
34. 34.Use (a + b)² = a² + 2ab + b² to find 22².
35. 35.Use a² − b² = (a + b)(a − b) to find 65² − 34².
36. 36.Find the value of x² − y² when x = 6 and y = 3.
37. 37.If a + b = 7 and ab = 12, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 19².
39. 39.Find the value of x² − 2xy + y² when x = 7 and y = 2.
40. 40.Find the value of x² − 2xy + y² when x = 13 and y = 9.

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