Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 170 · 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 = 10 and ab = 16, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 85².
3. 3.Use a² − b² = (a + b)(a − b) to find 46² − 24².
4. 4.Use (a − b)² = a² − 2ab + b² to find 21².
5. 5.Use (a + b)² = a² + 2ab + b² to find 66².
6. 6.Use (a + b)(a − b) = a² − b² to find 84 × 76.
7. 7.Use (a − b)² = a² − 2ab + b² to find 11².
8. 8.Use (a − b)² = a² − 2ab + b² to find 25².
9. 9.Find the value of x² + 2xy + y² when x = 10 and y = 2.
10. 10.Find the value of x² − 2xy + y² when x = 13 and y = 4.
11. 11.If a − b = 1 and ab = 42, what is a² + b²?
12. 12.If a + b = 9 and ab = 18, what is a² + b²?
13. 13.Find the value of x² + 2xy + y² when x = 12 and y = 5.
14. 14.Use (a − b)² = a² − 2ab + b² to find 59².
15. 15.If a − b = 2 and ab = 99, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 47 × 33.
17. 17.Use (a + b)² = a² + 2ab + b² to find 68².
18. 18.Use (a − b)² = a² − 2ab + b² to find 92².
19. 19.Use (a − b)² = a² − 2ab + b² to find 37².
20. 20.Find the value of x² − 2xy + y² when x = 11 and y = 4.
21. 21.Find the value of x² − 2xy + y² when x = 7 and y = 1.
22. 22.If a − b = 8 and ab = 20, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 31 × 29.
24. 24.Use a² − b² = (a + b)(a − b) to find 79² − 1².
25. 25.Use (a + b)² = a² + 2ab + b² to find 82².
26. 26.Use a² − b² = (a + b)(a − b) to find 53² − 12².
27. 27.Find the value of x² − 2xy + y² when x = 12 and y = 7.
28. 28.Use (a + b)(a − b) = a² − b² to find 42 × 38.
29. 29.Use a² − b² = (a + b)(a − b) to find 23² − 22².
30. 30.Use (a + b)² = a² + 2ab + b² to find 41².
31. 31.Use (a − b)² = a² − 2ab + b² to find 87².
32. 32.Use a² − b² = (a + b)(a − b) to find 75² − 72².
33. 33.Use a² − b² = (a + b)(a − b) to find 29² − 11².
34. 34.Use (a − b)² = a² − 2ab + b² to find 24².
35. 35.Use (a − b)² = a² − 2ab + b² to find 73².
36. 36.Use (a + b)² = a² + 2ab + b² to find 72².
37. 37.Use (a − b)² = a² − 2ab + b² to find 43².
38. 38.Use (a + b)(a − b) = a² − b² to find 27 × 13.
39. 39.Use a² − b² = (a + b)(a − b) to find 58² − 8².
40. 40.Use (a + b)(a − b) = a² − b² to find 21 × 19.

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