Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 174 · 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 107 × 93.
2. 2.If a − b = 1 and ab = 72, what is a² + b²?
3. 3.If a − b = 7 and ab = 44, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 99².
5. 5.Use (a + b)² = a² + 2ab + b² to find 46².
6. 6.Use (a + b)(a − b) = a² − b² to find 22 × 18.
7. 7.If a − b = 4 and ab = 12, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 91² − 45².
9. 9.Use (a − b)² = a² − 2ab + b² to find 28².
10. 10.Use (a − b)² = a² − 2ab + b² to find 83².
11. 11.Use (a + b)² = a² + 2ab + b² to find 24².
12. 12.If a − b = 1 and ab = 20, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 13².
14. 14.Use (a + b)(a − b) = a² − b² to find 43 × 37.
15. 15.Use (a − b)² = a² − 2ab + b² to find 61².
16. 16.Use (a − b)² = a² − 2ab + b² to find 37².
17. 17.Use a² − b² = (a + b)(a − b) to find 22² − 1².
18. 18.Use a² − b² = (a + b)(a − b) to find 49² − 9².
19. 19.Use (a + b)² = a² + 2ab + b² to find 51².
20. 20.Use a² − b² = (a + b)(a − b) to find 61² − 24².
21. 21.Use (a + b)² = a² + 2ab + b² to find 108².
22. 22.Use (a + b)(a − b) = a² − b² to find 34 × 26.
23. 23.If a + b = 18 and ab = 77, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 52².
25. 25.Use a² − b² = (a + b)(a − b) to find 64² − 33².
26. 26.Use a² − b² = (a + b)(a − b) to find 57² − 55².
27. 27.Use (a + b)(a − b) = a² − b² to find 49 × 31.
28. 28.Use (a + b)(a − b) = a² − b² to find 59 × 41.
29. 29.Find the value of x² − 2xy + y² when x = 7 and y = 2.
30. 30.Find the value of x² − y² when x = 8 and y = 3.
31. 31.Use a² − b² = (a + b)(a − b) to find 41² − 39².
32. 32.Use (a + b)² = a² + 2ab + b² to find 57².
33. 33.Find the value of x² + 2xy + y² when x = 4 and y = 1.
34. 34.Use a² − b² = (a + b)(a − b) to find 28² − 7².
35. 35.If a − b = 9 and ab = 22, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 56 × 44.
37. 37.Find the value of x² − 2xy + y² when x = 8 and y = 7.
38. 38.If a + b = 6 and ab = 8, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 91².
40. 40.Use (a + b)(a − b) = a² − b² to find 65 × 55.

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