Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 974 · 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)(a − b) = a² − b² to find 103 × 97.
2. 2.Use (a − b)² = a² − 2ab + b² to find 29².
3. 3.Use (a + b)(a − b) = a² − b² to find 33 × 27.
4. 4.Use (a + b)² = a² + 2ab + b² to find 45².
5. 5.Use a² − b² = (a + b)(a − b) to find 83² − 11².
6. 6.Use a² − b² = (a + b)(a − b) to find 62² − 60².
7. 7.Use (a + b)(a − b) = a² − b² to find 54 × 46.
8. 8.Use (a + b)(a − b) = a² − b² to find 43 × 37.
9. 9.Use (a + b)² = a² + 2ab + b² to find 35².
10. 10.Use (a + b)² = a² + 2ab + b² to find 21².
11. 11.If a + b = 19 and ab = 84, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 59².
13. 13.If a + b = 7 and ab = 12, what is a² + b²?
14. 14.If a + b = 6 and ab = 8, what is a² + b²?
15. 15.If a − b = 3 and ab = 28, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 67².
17. 17.Use (a + b)(a − b) = a² − b² to find 21 × 19.
18. 18.Use (a + b)(a − b) = a² − b² to find 32 × 28.
19. 19.Use (a + b)(a − b) = a² − b² to find 64 × 56.
20. 20.Use a² − b² = (a + b)(a − b) to find 86² − 39².
21. 21.Find the value of x² − y² when x = 6 and y = 1.
22. 22.Find the value of x² + 2xy + y² when x = 5 and y = 2.
23. 23.Find the value of x² − 2xy + y² when x = 15 and y = 9.
24. 24.If a − b = 2 and ab = 63, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 12 and y = 8.
26. 26.Use (a + b)(a − b) = a² − b² to find 61 × 59.
27. 27.Use a² − b² = (a + b)(a − b) to find 91² − 49².
28. 28.Use (a + b)² = a² + 2ab + b² to find 34².
29. 29.If a − b = 4 and ab = 5, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 43² − 11².
31. 31.Use (a + b)(a − b) = a² − b² to find 29 × 11.
32. 32.If a + b = 3 and ab = 2, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 67².
34. 34.Use (a + b)(a − b) = a² − b² to find 35 × 25.
35. 35.Use (a + b)(a − b) = a² − b² to find 73 × 67.
36. 36.Use (a + b)² = a² + 2ab + b² to find 95².
37. 37.Find the value of x² + 2xy + y² when x = 11 and y = 1.
38. 38.Use a² − b² = (a + b)(a − b) to find 55² − 1².
39. 39.Use (a − b)² = a² − 2ab + b² to find 17².
40. 40.Use (a − b)² = a² − 2ab + b² to find 28².

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