Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 575 · 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 42².
3. 3.Use (a − b)² = a² − 2ab + b² to find 43².
4. 4.Use (a + b)² = a² + 2ab + b² to find 53².
5. 5.Find the value of x² − 2xy + y² when x = 13 and y = 12.
6. 6.Use a² − b² = (a + b)(a − b) to find 62² − 6².
7. 7.Use (a + b)² = a² + 2ab + b² to find 86².
8. 8.Use (a + b)² = a² + 2ab + b² to find 79².
9. 9.If a − b = 2 and ab = 120, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 26².
11. 11.Use (a − b)² = a² − 2ab + b² to find 15².
12. 12.Use a² − b² = (a + b)(a − b) to find 85² − 14².
13. 13.Find the value of x² − y² when x = 10 and y = 7.
14. 14.Use a² − b² = (a + b)(a − b) to find 42² − 19².
15. 15.Find the value of x² − y² when x = 4 and y = 1.
16. 16.Use (a − b)² = a² − 2ab + b² to find 38².
17. 17.Find the value of x² − y² when x = 10 and y = 8.
18. 18.Find the value of x² + 2xy + y² when x = 12 and y = 1.
19. 19.Use (a + b)(a − b) = a² − b² to find 67 × 53.
20. 20.Use a² − b² = (a + b)(a − b) to find 73² − 1².
21. 21.Find the value of x² − 2xy + y² when x = 10 and y = 8.
22. 22.Use (a + b)² = a² + 2ab + b² to find 101².
23. 23.Use a² − b² = (a + b)(a − b) to find 42² − 8².
24. 24.Use (a + b)(a − b) = a² − b² to find 105 × 95.
25. 25.Find the value of x² − 2xy + y² when x = 10 and y = 4.
26. 26.Use (a + b)(a − b) = a² − b² to find 64 × 56.
27. 27.Use (a − b)² = a² − 2ab + b² to find 88².
28. 28.Use (a + b)² = a² + 2ab + b² to find 32².
29. 29.Find the value of x² + 2xy + y² when x = 6 and y = 5.
30. 30.Use (a − b)² = a² − 2ab + b² to find 76².
31. 31.If a + b = 5 and ab = 6, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 17².
33. 33.Find the value of x² − 2xy + y² when x = 15 and y = 3.
34. 34.Use a² − b² = (a + b)(a − b) to find 38² − 17².
35. 35.Use (a − b)² = a² − 2ab + b² to find 99².
36. 36.Use (a − b)² = a² − 2ab + b² to find 12².
37. 37.If a − b = 1 and ab = 72, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 54².
39. 39.If a + b = 4 and ab = 3, what is a² + b²?
40. 40.Find the value of x² − 2xy + y² when x = 7 and y = 6.

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