Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 475 · 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.Find the value of x² − 2xy + y² when x = 10 and y = 8.
2. 2.If a − b = 1 and ab = 30, what is a² + b²?
3. 3.If a − b = 2 and ab = 80, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 63² − 5².
5. 5.Use (a + b)² = a² + 2ab + b² to find 84².
6. 6.Use (a − b)² = a² − 2ab + b² to find 32².
7. 7.Find the value of x² + 2xy + y² when x = 9 and y = 7.
8. 8.Use a² − b² = (a + b)(a − b) to find 91² − 25².
9. 9.Use (a + b)(a − b) = a² − b² to find 93 × 87.
10. 10.Use (a + b)² = a² + 2ab + b² to find 13².
11. 11.Find the value of x² + 2xy + y² when x = 7 and y = 6.
12. 12.Find the value of x² − y² when x = 12 and y = 11.
13. 13.Use a² − b² = (a + b)(a − b) to find 32² − 15².
14. 14.Use (a + b)(a − b) = a² − b² to find 24 × 16.
15. 15.Find the value of x² − y² when x = 12 and y = 3.
16. 16.If a + b = 9 and ab = 18, what is a² + b²?
17. 17.If a − b = 7 and ab = 30, what is a² + b²?
18. 18.Find the value of x² − 2xy + y² when x = 5 and y = 1.
19. 19.Use (a − b)² = a² − 2ab + b² to find 39².
20. 20.Find the value of x² + 2xy + y² when x = 13 and y = 3.
21. 21.If a + b = 16 and ab = 63, what is a² + b²?
22. 22.If a − b = 2 and ab = 3, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 21².
24. 24.Use (a + b)² = a² + 2ab + b² to find 12².
25. 25.Use a² − b² = (a + b)(a − b) to find 52² − 46².
26. 26.If a − b = 1 and ab = 132, what is a² + b²?
27. 27.Find the value of x² + 2xy + y² when x = 5 and y = 3.
28. 28.Find the value of x² + 2xy + y² when x = 3 and y = 1.
29. 29.Use (a + b)² = a² + 2ab + b² to find 79².
30. 30.Use (a + b)² = a² + 2ab + b² to find 32².
31. 31.If a + b = 4 and ab = 3, what is a² + b²?
32. 32.Find the value of x² − 2xy + y² when x = 8 and y = 4.
33. 33.Use (a + b)(a − b) = a² − b² to find 63 × 57.
34. 34.Use a² − b² = (a + b)(a − b) to find 73² − 29².
35. 35.If a − b = 1 and ab = 72, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 27² − 9².
37. 37.Use (a − b)² = a² − 2ab + b² to find 41².
38. 38.Find the value of x² − y² when x = 5 and y = 4.
39. 39.Use (a − b)² = a² − 2ab + b² to find 82².
40. 40.Use (a + b)(a − b) = a² − b² to find 59 × 41.

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