Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 149 · 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 = 4 and ab = 77, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 20² − 11².
3. 3.Use a² − b² = (a + b)(a − b) to find 83² − 26².
4. 4.Find the value of x² − y² when x = 4 and y = 1.
5. 5.Use (a + b)(a − b) = a² − b² to find 41 × 39.
6. 6.If a + b = 19 and ab = 90, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 38² − 10².
8. 8.Use (a − b)² = a² − 2ab + b² to find 79².
9. 9.Use (a + b)² = a² + 2ab + b² to find 42².
10. 10.Use (a + b)(a − b) = a² − b² to find 25 × 15.
11. 11.Find the value of x² − y² when x = 3 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 59² − 32².
13. 13.If a − b = 1 and ab = 132, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 105².
15. 15.Use (a + b)² = a² + 2ab + b² to find 93².
16. 16.If a − b = 1 and ab = 42, what is a² + b²?
17. 17.Find the value of x² + 2xy + y² when x = 5 and y = 2.
18. 18.Find the value of x² + 2xy + y² when x = 4 and y = 2.
19. 19.Use (a − b)² = a² − 2ab + b² to find 75².
20. 20.If a + b = 4 and ab = 3, what is a² + b²?
21. 21.If a − b = 2 and ab = 99, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 12².
23. 23.If a + b = 18 and ab = 72, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 87² − 34².
25. 25.If a − b = 5 and ab = 14, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 57².
27. 27.Use (a + b)(a − b) = a² − b² to find 75 × 65.
28. 28.Use (a − b)² = a² − 2ab + b² to find 38².
29. 29.Use (a + b)(a − b) = a² − b² to find 63 × 57.
30. 30.If a + b = 6 and ab = 5, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 31².
32. 32.Use (a + b)² = a² + 2ab + b² to find 101².
33. 33.If a − b = 4 and ab = 5, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 58 × 42.
35. 35.Use a² − b² = (a + b)(a − b) to find 44² − 37².
36. 36.Find the value of x² − 2xy + y² when x = 14 and y = 8.
37. 37.If a − b = 4 and ab = 21, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 76 × 64.
39. 39.Use (a − b)² = a² − 2ab + b² to find 94².
40. 40.Use a² − b² = (a + b)(a − b) to find 91² − 13².

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