Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 39 · 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)(a − b) = a² − b² to find 44 × 36.
2. 2.Use (a + b)² = a² + 2ab + b² to find 84².
3. 3.Use (a − b)² = a² − 2ab + b² to find 13².
4. 4.Find the value of x² − 2xy + y² when x = 13 and y = 8.
5. 5.Use (a + b)² = a² + 2ab + b² to find 108².
6. 6.Use (a + b)(a − b) = a² − b² to find 98 × 82.
7. 7.Use (a − b)² = a² − 2ab + b² to find 54².
8. 8.Use (a − b)² = a² − 2ab + b² to find 69².
9. 9.Use (a + b)(a − b) = a² − b² to find 23 × 17.
10. 10.Use (a + b)(a − b) = a² − b² to find 73 × 67.
11. 11.If a + b = 19 and ab = 88, what is a² + b²?
12. 12.If a + b = 4 and ab = 3, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 17².
14. 14.Use (a + b)² = a² + 2ab + b² to find 38².
15. 15.If a + b = 9 and ab = 18, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 93 × 87.
17. 17.Find the value of x² − 2xy + y² when x = 12 and y = 4.
18. 18.Use (a + b)(a − b) = a² − b² to find 82 × 78.
19. 19.Use (a + b)² = a² + 2ab + b² to find 12².
20. 20.Find the value of x² − y² when x = 3 and y = 2.
21. 21.If a + b = 11 and ab = 24, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 49 × 31.
23. 23.Use (a + b)² = a² + 2ab + b² to find 101².
24. 24.Use (a + b)² = a² + 2ab + b² to find 93².
25. 25.Use (a + b)² = a² + 2ab + b² to find 73².
26. 26.Use (a − b)² = a² − 2ab + b² to find 48².
27. 27.If a + b = 9 and ab = 14, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 39² − 24².
29. 29.Use (a + b)(a − b) = a² − b² to find 105 × 95.
30. 30.Find the value of x² + 2xy + y² when x = 6 and y = 5.
31. 31.Use (a + b)(a − b) = a² − b² to find 67 × 53.
32. 32.Use (a − b)² = a² − 2ab + b² to find 52².
33. 33.Find the value of x² − y² when x = 8 and y = 7.
34. 34.Use (a + b)(a − b) = a² − b² to find 85 × 75.
35. 35.Find the value of x² − 2xy + y² when x = 15 and y = 1.
36. 36.Find the value of x² − 2xy + y² when x = 7 and y = 4.
37. 37.Find the value of x² + 2xy + y² when x = 4 and y = 3.
38. 38.Use (a + b)(a − b) = a² − b² to find 52 × 48.
39. 39.Use a² − b² = (a + b)(a − b) to find 26² − 12².
40. 40.Find the value of x² − 2xy + y² when x = 3 and y = 1.

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