Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 455 · 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 89².
2. 2.Use a² − b² = (a + b)(a − b) to find 69² − 50².
3. 3.If a − b = 3 and ab = 4, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 32².
5. 5.Use (a + b)(a − b) = a² − b² to find 72 × 68.
6. 6.Use (a + b)(a − b) = a² − b² to find 73 × 67.
7. 7.Use a² − b² = (a + b)(a − b) to find 33² − 21².
8. 8.Use (a + b)(a − b) = a² − b² to find 29 × 11.
9. 9.Use (a + b)(a − b) = a² − b² to find 102 × 98.
10. 10.Use (a − b)² = a² − 2ab + b² to find 28².
11. 11.Use (a + b)² = a² + 2ab + b² to find 33².
12. 12.Use (a − b)² = a² − 2ab + b² to find 85².
13. 13.Use a² − b² = (a + b)(a − b) to find 78² − 1².
14. 14.Use (a + b)(a − b) = a² − b² to find 28 × 12.
15. 15.If a + b = 5 and ab = 4, what is a² + b²?
16. 16.Find the value of x² − y² when x = 5 and y = 2.
17. 17.Use (a + b)² = a² + 2ab + b² to find 65².
18. 18.If a − b = 1 and ab = 6, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 43².
20. 20.Use a² − b² = (a + b)(a − b) to find 83² − 12².
21. 21.If a + b = 9 and ab = 18, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 47².
23. 23.If a + b = 9 and ab = 14, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 37².
25. 25.Use (a + b)(a − b) = a² − b² to find 83 × 77.
26. 26.Use (a + b)² = a² + 2ab + b² to find 23².
27. 27.If a − b = 5 and ab = 14, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 50² − 1².
29. 29.Use (a + b)² = a² + 2ab + b² to find 99².
30. 30.If a − b = 3 and ab = 10, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 87².
32. 32.Use (a + b)² = a² + 2ab + b² to find 54².
33. 33.Use (a + b)(a − b) = a² − b² to find 91 × 89.
34. 34.Use (a − b)² = a² − 2ab + b² to find 38².
35. 35.Use (a + b)(a − b) = a² − b² to find 24 × 16.
36. 36.If a − b = 3 and ab = 54, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 41 × 39.
38. 38.Use (a + b)² = a² + 2ab + b² to find 63².
39. 39.Use a² − b² = (a + b)(a − b) to find 42² − 5².
40. 40.Use (a + b)² = a² + 2ab + b² to find 22².

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