Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 948 · 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 = 3 and y = 2.
2. 2.Find the value of x² + 2xy + y² when x = 5 and y = 1.
3. 3.Use (a + b)(a − b) = a² − b² to find 89 × 71.
4. 4.Use (a + b)² = a² + 2ab + b² to find 62².
5. 5.Use (a + b)(a − b) = a² − b² to find 61 × 59.
6. 6.Find the value of x² − y² when x = 3 and y = 2.
7. 7.Use (a + b)(a − b) = a² − b² to find 59 × 41.
8. 8.Use (a − b)² = a² − 2ab + b² to find 33².
9. 9.Use (a + b)² = a² + 2ab + b² to find 54².
10. 10.Use (a − b)² = a² − 2ab + b² to find 87².
11. 11.Use (a + b)² = a² + 2ab + b² to find 94².
12. 12.Find the value of x² + 2xy + y² when x = 7 and y = 5.
13. 13.Use (a − b)² = a² − 2ab + b² to find 69².
14. 14.Use (a + b)² = a² + 2ab + b² to find 68².
15. 15.Use a² − b² = (a + b)(a − b) to find 85² − 7².
16. 16.Use (a − b)² = a² − 2ab + b² to find 98².
17. 17.Use (a + b)² = a² + 2ab + b² to find 77².
18. 18.Find the value of x² + 2xy + y² when x = 8 and y = 4.
19. 19.If a + b = 7 and ab = 12, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 96².
21. 21.Use (a + b)² = a² + 2ab + b² to find 37².
22. 22.Find the value of x² − y² when x = 15 and y = 4.
23. 23.Use (a + b)² = a² + 2ab + b² to find 39².
24. 24.Find the value of x² + 2xy + y² when x = 15 and y = 13.
25. 25.If a + b = 17 and ab = 66, what is a² + b²?
26. 26.If a + b = 15 and ab = 56, what is a² + b²?
27. 27.Find the value of x² + 2xy + y² when x = 14 and y = 4.
28. 28.Find the value of x² − y² when x = 12 and y = 10.
29. 29.Find the value of x² + 2xy + y² when x = 14 and y = 2.
30. 30.Use (a − b)² = a² − 2ab + b² to find 51².
31. 31.Use a² − b² = (a + b)(a − b) to find 39² − 18².
32. 32.Use (a − b)² = a² − 2ab + b² to find 42².
33. 33.Find the value of x² + 2xy + y² when x = 4 and y = 3.
34. 34.If a − b = 2 and ab = 15, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 67 × 53.
36. 36.Use (a + b)² = a² + 2ab + b² to find 103².
37. 37.Find the value of x² − 2xy + y² when x = 13 and y = 6.
38. 38.Use (a − b)² = a² − 2ab + b² to find 64².
39. 39.Use (a + b)(a − b) = a² − b² to find 38 × 22.
40. 40.If a + b = 3 and ab = 2, what is a² + b²?

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