Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 904 · 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)(a − b) = a² − b² to find 69 × 51.
2. 2.Use (a + b)(a − b) = a² − b² to find 35 × 25.
3. 3.Use a² − b² = (a + b)(a − b) to find 69² − 7².
4. 4.Find the value of x² + 2xy + y² when x = 5 and y = 3.
5. 5.If a − b = 2 and ab = 3, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 33².
7. 7.Use (a + b)(a − b) = a² − b² to find 24 × 16.
8. 8.Use a² − b² = (a + b)(a − b) to find 81² − 76².
9. 9.Use (a + b)(a − b) = a² − b² to find 28 × 12.
10. 10.Use a² − b² = (a + b)(a − b) to find 95² − 2².
11. 11.Use a² − b² = (a + b)(a − b) to find 39² − 18².
12. 12.Use a² − b² = (a + b)(a − b) to find 51² − 13².
13. 13.If a + b = 11 and ab = 30, what is a² + b²?
14. 14.If a + b = 5 and ab = 6, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 34².
16. 16.Use (a + b)(a − b) = a² − b² to find 82 × 78.
17. 17.Find the value of x² + 2xy + y² when x = 4 and y = 1.
18. 18.Find the value of x² + 2xy + y² when x = 14 and y = 1.
19. 19.Find the value of x² − y² when x = 3 and y = 2.
20. 20.Use (a + b)² = a² + 2ab + b² to find 87².
21. 21.Use (a − b)² = a² − 2ab + b² to find 99².
22. 22.Find the value of x² − y² when x = 9 and y = 1.
23. 23.Use (a + b)² = a² + 2ab + b² to find 61².
24. 24.Use (a − b)² = a² − 2ab + b² to find 58².
25. 25.Find the value of x² + 2xy + y² when x = 3 and y = 2.
26. 26.Use a² − b² = (a + b)(a − b) to find 41² − 30².
27. 27.Use (a − b)² = a² − 2ab + b² to find 28².
28. 28.Use (a + b)(a − b) = a² − b² to find 55 × 45.
29. 29.If a + b = 3 and ab = 2, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 39 × 21.
31. 31.If a − b = 5 and ab = 24, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 61 × 59.
33. 33.Use (a + b)(a − b) = a² − b² to find 23 × 17.
34. 34.Use a² − b² = (a + b)(a − b) to find 94² − 59².
35. 35.Use (a + b)² = a² + 2ab + b² to find 31².
36. 36.Use (a + b)² = a² + 2ab + b² to find 36².
37. 37.Find the value of x² − y² when x = 5 and y = 1.
38. 38.Use (a + b)² = a² + 2ab + b² to find 55².
39. 39.Find the value of x² − 2xy + y² when x = 8 and y = 2.
40. 40.Use (a + b)(a − b) = a² − b² to find 92 × 88.

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