Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 454 · 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 16².
2. 2.Use (a + b)(a − b) = a² − b² to find 43 × 37.
3. 3.Use (a + b)(a − b) = a² − b² to find 88 × 72.
4. 4.Find the value of x² + 2xy + y² when x = 11 and y = 3.
5. 5.Use (a − b)² = a² − 2ab + b² to find 79².
6. 6.Use (a + b)² = a² + 2ab + b² to find 14².
7. 7.Use (a + b)² = a² + 2ab + b² to find 104².
8. 8.Find the value of x² − 2xy + y² when x = 7 and y = 5.
9. 9.Use (a + b)² = a² + 2ab + b² to find 105².
10. 10.If a + b = 9 and ab = 18, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 73².
12. 12.Use (a − b)² = a² − 2ab + b² to find 96².
13. 13.If a − b = 5 and ab = 66, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 61².
15. 15.Use (a + b)(a − b) = a² − b² to find 66 × 54.
16. 16.Use a² − b² = (a + b)(a − b) to find 91² − 56².
17. 17.Use (a + b)(a − b) = a² − b² to find 35 × 25.
18. 18.Find the value of x² − y² when x = 14 and y = 3.
19. 19.Use (a + b)² = a² + 2ab + b² to find 75².
20. 20.Use (a + b)² = a² + 2ab + b² to find 37².
21. 21.Use (a + b)(a − b) = a² − b² to find 42 × 38.
22. 22.Use (a + b)(a − b) = a² − b² to find 78 × 62.
23. 23.Use (a + b)(a − b) = a² − b² to find 53 × 47.
24. 24.Use a² − b² = (a + b)(a − b) to find 65² − 8².
25. 25.Use (a + b)(a − b) = a² − b² to find 93 × 87.
26. 26.Use (a + b)(a − b) = a² − b² to find 59 × 41.
27. 27.Find the value of x² − y² when x = 5 and y = 4.
28. 28.Use (a + b)(a − b) = a² − b² to find 58 × 42.
29. 29.Use (a + b)² = a² + 2ab + b² to find 84².
30. 30.Use (a − b)² = a² − 2ab + b² to find 63².
31. 31.If a − b = 6 and ab = 27, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 86 × 74.
33. 33.Use (a − b)² = a² − 2ab + b² to find 43².
34. 34.Use (a + b)² = a² + 2ab + b² to find 63².
35. 35.Use (a + b)(a − b) = a² − b² to find 82 × 78.
36. 36.Use (a + b)(a − b) = a² − b² to find 55 × 45.
37. 37.Find the value of x² − 2xy + y² when x = 3 and y = 1.
38. 38.If a + b = 17 and ab = 70, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 54 × 46.
40. 40.Use (a + b)² = a² + 2ab + b² to find 36².

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