Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 318 · 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 = 3.
2. 2.Use (a + b)² = a² + 2ab + b² to find 49².
3. 3.Find the value of x² + 2xy + y² when x = 14 and y = 3.
4. 4.If a − b = 5 and ab = 36, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 27².
6. 6.Find the value of x² + 2xy + y² when x = 3 and y = 2.
7. 7.Use (a + b)(a − b) = a² − b² to find 32 × 28.
8. 8.Use (a + b)² = a² + 2ab + b² to find 93².
9. 9.Use (a − b)² = a² − 2ab + b² to find 12².
10. 10.Use (a − b)² = a² − 2ab + b² to find 53².
11. 11.Use (a + b)² = a² + 2ab + b² to find 74².
12. 12.Use (a + b)(a − b) = a² − b² to find 98 × 82.
13. 13.If a − b = 3 and ab = 88, what is a² + b²?
14. 14.Find the value of x² + 2xy + y² when x = 5 and y = 1.
15. 15.Use (a + b)(a − b) = a² − b² to find 45 × 35.
16. 16.Use (a + b)² = a² + 2ab + b² to find 72².
17. 17.Find the value of x² + 2xy + y² when x = 6 and y = 1.
18. 18.Use (a + b)² = a² + 2ab + b² to find 101².
19. 19.Use a² − b² = (a + b)(a − b) to find 23² − 22².
20. 20.Use (a + b)(a − b) = a² − b² to find 82 × 78.
21. 21.Find the value of x² − y² when x = 9 and y = 8.
22. 22.Use a² − b² = (a + b)(a − b) to find 20² − 19².
23. 23.Use (a + b)² = a² + 2ab + b² to find 98².
24. 24.Use (a − b)² = a² − 2ab + b² to find 19².
25. 25.Use (a + b)(a − b) = a² − b² to find 63 × 57.
26. 26.Find the value of x² + 2xy + y² when x = 11 and y = 2.
27. 27.Use (a + b)² = a² + 2ab + b² to find 35².
28. 28.Use (a − b)² = a² − 2ab + b² to find 85².
29. 29.If a + b = 6 and ab = 8, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 89² − 7².
31. 31.Use (a + b)(a − b) = a² − b² to find 69 × 51.
32. 32.Find the value of x² − y² when x = 15 and y = 13.
33. 33.Use (a + b)² = a² + 2ab + b² to find 41².
34. 34.Use (a + b)² = a² + 2ab + b² to find 68².
35. 35.Use (a + b)(a − b) = a² − b² to find 57 × 43.
36. 36.Use (a + b)(a − b) = a² − b² to find 21 × 19.
37. 37.Use (a + b)² = a² + 2ab + b² to find 28².
38. 38.Find the value of x² + 2xy + y² when x = 11 and y = 1.
39. 39.Use a² − b² = (a + b)(a − b) to find 77² − 29².
40. 40.Find the value of x² + 2xy + y² when x = 15 and y = 4.

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