Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 673 · 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.If a + b = 15 and ab = 56, what is a² + b²?
2. 2.Find the value of x² − y² when x = 11 and y = 6.
3. 3.Use (a + b)(a − b) = a² − b² to find 91 × 89.
4. 4.Find the value of x² + 2xy + y² when x = 5 and y = 1.
5. 5.Find the value of x² − y² when x = 12 and y = 3.
6. 6.Use (a + b)² = a² + 2ab + b² to find 59².
7. 7.Use (a + b)² = a² + 2ab + b² to find 93².
8. 8.If a − b = 4 and ab = 5, what is a² + b²?
9. 9.Find the value of x² − y² when x = 5 and y = 2.
10. 10.Use a² − b² = (a + b)(a − b) to find 61² − 36².
11. 11.Use (a − b)² = a² − 2ab + b² to find 12².
12. 12.Use (a + b)² = a² + 2ab + b² to find 109².
13. 13.Find the value of x² + 2xy + y² when x = 11 and y = 7.
14. 14.Use (a + b)² = a² + 2ab + b² to find 99².
15. 15.Use (a − b)² = a² − 2ab + b² to find 47².
16. 16.Use a² − b² = (a + b)(a − b) to find 49² − 23².
17. 17.Use (a + b)(a − b) = a² − b² to find 48 × 32.
18. 18.Find the value of x² − 2xy + y² when x = 6 and y = 1.
19. 19.Use a² − b² = (a + b)(a − b) to find 37² − 12².
20. 20.Find the value of x² + 2xy + y² when x = 7 and y = 3.
21. 21.Use (a + b)² = a² + 2ab + b² to find 64².
22. 22.If a − b = 1 and ab = 12, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 34² − 9².
24. 24.Use (a + b)² = a² + 2ab + b² to find 91².
25. 25.If a + b = 3 and ab = 2, what is a² + b²?
26. 26.If a − b = 3 and ab = 40, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 32 × 28.
28. 28.Use (a − b)² = a² − 2ab + b² to find 76².
29. 29.Use (a + b)² = a² + 2ab + b² to find 58².
30. 30.If a − b = 7 and ab = 44, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 28² − 25².
32. 32.Use a² − b² = (a + b)(a − b) to find 42² − 7².
33. 33.Use (a − b)² = a² − 2ab + b² to find 57².
34. 34.Use (a − b)² = a² − 2ab + b² to find 11².
35. 35.If a + b = 11 and ab = 30, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 87 × 73.
37. 37.Use a² − b² = (a + b)(a − b) to find 24² − 19².
38. 38.Use a² − b² = (a + b)(a − b) to find 58² − 11².
39. 39.If a + b = 13 and ab = 40, what is a² + b²?
40. 40.Find the value of x² + 2xy + y² when x = 10 and y = 4.

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