Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 300 · 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 56².
2. 2.Use (a + b)² = a² + 2ab + b² to find 105².
3. 3.Use (a + b)(a − b) = a² − b² to find 67 × 53.
4. 4.Use (a + b)(a − b) = a² − b² to find 61 × 59.
5. 5.Use (a + b)² = a² + 2ab + b² to find 104².
6. 6.If a + b = 16 and ab = 48, what is a² + b²?
7. 7.Find the value of x² + 2xy + y² when x = 4 and y = 2.
8. 8.Use (a + b)(a − b) = a² − b² to find 24 × 16.
9. 9.If a − b = 1 and ab = 20, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 15².
11. 11.Use (a + b)² = a² + 2ab + b² to find 101².
12. 12.If a + b = 7 and ab = 12, what is a² + b²?
13. 13.If a − b = 1 and ab = 6, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 67².
15. 15.Use (a + b)² = a² + 2ab + b² to find 39².
16. 16.Use (a + b)² = a² + 2ab + b² to find 28².
17. 17.Use (a + b)² = a² + 2ab + b² to find 91².
18. 18.Use a² − b² = (a + b)(a − b) to find 93² − 82².
19. 19.Use (a + b)² = a² + 2ab + b² to find 52².
20. 20.Use (a + b)² = a² + 2ab + b² to find 78².
21. 21.Use a² − b² = (a + b)(a − b) to find 63² − 58².
22. 22.Use (a + b)² = a² + 2ab + b² to find 58².
23. 23.Use a² − b² = (a + b)(a − b) to find 88² − 73².
24. 24.Find the value of x² + 2xy + y² when x = 4 and y = 1.
25. 25.Use (a − b)² = a² − 2ab + b² to find 64².
26. 26.Use (a − b)² = a² − 2ab + b² to find 63².
27. 27.Use (a + b)² = a² + 2ab + b² to find 56².
28. 28.Use (a + b)(a − b) = a² − b² to find 104 × 96.
29. 29.Use (a + b)² = a² + 2ab + b² to find 23².
30. 30.If a − b = 1 and ab = 72, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 103².
32. 32.Use (a + b)² = a² + 2ab + b² to find 11².
33. 33.Use (a + b)² = a² + 2ab + b² to find 21².
34. 34.Find the value of x² + 2xy + y² when x = 7 and y = 6.
35. 35.Use (a + b)(a − b) = a² − b² to find 39 × 21.
36. 36.Use a² − b² = (a + b)(a − b) to find 76² − 34².
37. 37.Use (a − b)² = a² − 2ab + b² to find 34².
38. 38.Use (a + b)² = a² + 2ab + b² to find 26².
39. 39.Find the value of x² − 2xy + y² when x = 5 and y = 2.
40. 40.Find the value of x² + 2xy + y² when x = 6 and y = 5.

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