Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 906 · 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 61².
2. 2.Use (a + b)(a − b) = a² − b² to find 36 × 24.
3. 3.Use (a − b)² = a² − 2ab + b² to find 21².
4. 4.If a − b = 4 and ab = 32, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 11 and y = 2.
6. 6.Use (a − b)² = a² − 2ab + b² to find 74².
7. 7.Use a² − b² = (a + b)(a − b) to find 60² − 3².
8. 8.If a + b = 9 and ab = 18, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 77² − 70².
10. 10.If a + b = 5 and ab = 4, what is a² + b²?
11. 11.Find the value of x² + 2xy + y² when x = 14 and y = 7.
12. 12.Use a² − b² = (a + b)(a − b) to find 37² − 28².
13. 13.Use a² − b² = (a + b)(a − b) to find 51² − 23².
14. 14.Use (a − b)² = a² − 2ab + b² to find 29².
15. 15.Use (a − b)² = a² − 2ab + b² to find 69².
16. 16.Find the value of x² + 2xy + y² when x = 14 and y = 2.
17. 17.Use a² − b² = (a + b)(a − b) to find 20² − 12².
18. 18.Find the value of x² − 2xy + y² when x = 6 and y = 5.
19. 19.Find the value of x² − y² when x = 3 and y = 2.
20. 20.Use (a + b)(a − b) = a² − b² to find 76 × 64.
21. 21.Use (a − b)² = a² − 2ab + b² to find 18².
22. 22.If a − b = 9 and ab = 22, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 28².
24. 24.Use a² − b² = (a + b)(a − b) to find 64² − 13².
25. 25.Use (a + b)² = a² + 2ab + b² to find 97².
26. 26.Use (a + b)(a − b) = a² − b² to find 54 × 46.
27. 27.Use (a − b)² = a² − 2ab + b² to find 17².
28. 28.Use (a + b)(a − b) = a² − b² to find 85 × 75.
29. 29.Use (a − b)² = a² − 2ab + b² to find 99².
30. 30.Use a² − b² = (a + b)(a − b) to find 39² − 7².
31. 31.Find the value of x² − 2xy + y² when x = 12 and y = 5.
32. 32.Use (a + b)² = a² + 2ab + b² to find 81².
33. 33.Use (a − b)² = a² − 2ab + b² to find 45².
34. 34.Use (a + b)(a − b) = a² − b² to find 26 × 14.
35. 35.Use a² − b² = (a + b)(a − b) to find 58² − 2².
36. 36.Use a² − b² = (a + b)(a − b) to find 76² − 11².
37. 37.Use (a + b)(a − b) = a² − b² to find 27 × 13.
38. 38.If a − b = 4 and ab = 12, what is a² + b²?
39. 39.If a − b = 5 and ab = 66, what is a² + b²?
40. 40.Find the value of x² + 2xy + y² when x = 7 and y = 1.

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