Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 271 · 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 a² − b² = (a + b)(a − b) to find 72² − 16².
2. 2.Use (a + b)² = a² + 2ab + b² to find 68².
3. 3.Find the value of x² − 2xy + y² when x = 13 and y = 2.
4. 4.If a + b = 12 and ab = 27, what is a² + b²?
5. 5.Find the value of x² − y² when x = 12 and y = 1.
6. 6.Use a² − b² = (a + b)(a − b) to find 27² − 22².
7. 7.Use (a − b)² = a² − 2ab + b² to find 18².
8. 8.Use (a + b)² = a² + 2ab + b² to find 103².
9. 9.Find the value of x² − y² when x = 10 and y = 1.
10. 10.Use (a + b)² = a² + 2ab + b² to find 92².
11. 11.Find the value of x² + 2xy + y² when x = 6 and y = 4.
12. 12.Use a² − b² = (a + b)(a − b) to find 29² − 5².
13. 13.If a + b = 11 and ab = 30, what is a² + b²?
14. 14.If a − b = 1 and ab = 6, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 39².
16. 16.Use (a + b)(a − b) = a² − b² to find 39 × 21.
17. 17.Use (a + b)(a − b) = a² − b² to find 24 × 16.
18. 18.If a − b = 3 and ab = 10, what is a² + b²?
19. 19.If a + b = 18 and ab = 80, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 98 × 82.
21. 21.If a − b = 4 and ab = 5, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 99 × 81.
23. 23.Use a² − b² = (a + b)(a − b) to find 40² − 24².
24. 24.If a + b = 16 and ab = 63, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 56².
26. 26.Use (a − b)² = a² − 2ab + b² to find 97².
27. 27.Use (a − b)² = a² − 2ab + b² to find 17².
28. 28.Use (a + b)(a − b) = a² − b² to find 66 × 54.
29. 29.Use (a + b)² = a² + 2ab + b² to find 31².
30. 30.Use (a + b)² = a² + 2ab + b² to find 84².
31. 31.Use (a + b)² = a² + 2ab + b² to find 33².
32. 32.Find the value of x² + 2xy + y² when x = 14 and y = 12.
33. 33.Use a² − b² = (a + b)(a − b) to find 61² − 47².
34. 34.If a − b = 5 and ab = 84, what is a² + b²?
35. 35.Find the value of x² − y² when x = 4 and y = 3.
36. 36.Use a² − b² = (a + b)(a − b) to find 83² − 4².
37. 37.Use a² − b² = (a + b)(a − b) to find 38² − 27².
38. 38.If a + b = 18 and ab = 77, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 34².
40. 40.Find the value of x² + 2xy + y² when x = 10 and y = 1.

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