Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 718 · 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 69².
2. 2.Use (a + b)² = a² + 2ab + b² to find 28².
3. 3.Use a² − b² = (a + b)(a − b) to find 70² − 30².
4. 4.If a − b = 1 and ab = 30, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 29².
6. 6.Use (a − b)² = a² − 2ab + b² to find 16².
7. 7.Use (a + b)² = a² + 2ab + b² to find 74².
8. 8.Use (a + b)² = a² + 2ab + b² to find 72².
9. 9.If a + b = 17 and ab = 72, what is a² + b²?
10. 10.If a − b = 4 and ab = 12, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 106 × 94.
12. 12.Use a² − b² = (a + b)(a − b) to find 78² − 53².
13. 13.Find the value of x² − 2xy + y² when x = 4 and y = 1.
14. 14.Use a² − b² = (a + b)(a − b) to find 38² − 34².
15. 15.Use (a + b)² = a² + 2ab + b² to find 27².
16. 16.Use (a + b)(a − b) = a² − b² to find 94 × 86.
17. 17.Use (a + b)(a − b) = a² − b² to find 73 × 67.
18. 18.Find the value of x² − y² when x = 5 and y = 1.
19. 19.Use (a − b)² = a² − 2ab + b² to find 25².
20. 20.Find the value of x² − 2xy + y² when x = 11 and y = 1.
21. 21.Use (a − b)² = a² − 2ab + b² to find 56².
22. 22.Use (a − b)² = a² − 2ab + b² to find 96².
23. 23.Find the value of x² + 2xy + y² when x = 8 and y = 5.
24. 24.Use (a + b)² = a² + 2ab + b² to find 84².
25. 25.If a − b = 7 and ab = 18, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 86 × 74.
27. 27.Find the value of x² + 2xy + y² when x = 5 and y = 1.
28. 28.Find the value of x² − y² when x = 11 and y = 9.
29. 29.If a + b = 13 and ab = 40, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 73².
31. 31.Use (a − b)² = a² − 2ab + b² to find 82².
32. 32.Find the value of x² + 2xy + y² when x = 8 and y = 7.
33. 33.Use (a + b)(a − b) = a² − b² to find 36 × 24.
34. 34.Use a² − b² = (a + b)(a − b) to find 92² − 72².
35. 35.Use (a + b)² = a² + 2ab + b² to find 23².
36. 36.Find the value of x² + 2xy + y² when x = 8 and y = 6.
37. 37.Use a² − b² = (a + b)(a − b) to find 33² − 20².
38. 38.Use (a − b)² = a² − 2ab + b² to find 95².
39. 39.Find the value of x² − 2xy + y² when x = 3 and y = 1.
40. 40.Use (a + b)² = a² + 2ab + b² to find 32².

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