Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 254 · 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 a² − b² = (a + b)(a − b) to find 55² − 15².
2. 2.Use a² − b² = (a + b)(a − b) to find 56² − 46².
3. 3.Use (a − b)² = a² − 2ab + b² to find 46².
4. 4.Find the value of x² + 2xy + y² when x = 6 and y = 3.
5. 5.Use (a + b)² = a² + 2ab + b² to find 17².
6. 6.Use (a + b)(a − b) = a² − b² to find 38 × 22.
7. 7.If a + b = 16 and ab = 55, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 30² − 1².
9. 9.If a + b = 11 and ab = 24, what is a² + b²?
10. 10.If a − b = 7 and ab = 30, what is a² + b²?
11. 11.Find the value of x² − 2xy + y² when x = 14 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 90² − 67².
13. 13.If a − b = 11 and ab = 12, what is a² + b²?
14. 14.Find the value of x² + 2xy + y² when x = 15 and y = 1.
15. 15.Find the value of x² + 2xy + y² when x = 11 and y = 2.
16. 16.Use (a + b)(a − b) = a² − b² to find 103 × 97.
17. 17.Use (a − b)² = a² − 2ab + b² to find 56².
18. 18.Use (a + b)(a − b) = a² − b² to find 86 × 74.
19. 19.Use (a + b)(a − b) = a² − b² to find 75 × 65.
20. 20.Use (a + b)(a − b) = a² − b² to find 82 × 78.
21. 21.Use (a − b)² = a² − 2ab + b² to find 53².
22. 22.Find the value of x² − y² when x = 5 and y = 2.
23. 23.Use a² − b² = (a + b)(a − b) to find 91² − 8².
24. 24.Use a² − b² = (a + b)(a − b) to find 26² − 23².
25. 25.Use (a + b)² = a² + 2ab + b² to find 58².
26. 26.Use (a − b)² = a² − 2ab + b² to find 35².
27. 27.If a − b = 7 and ab = 18, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 53² − 10².
29. 29.Use (a + b)² = a² + 2ab + b² to find 104².
30. 30.Use a² − b² = (a + b)(a − b) to find 77² − 51².
31. 31.Use (a + b)(a − b) = a² − b² to find 101 × 99.
32. 32.Use (a + b)(a − b) = a² − b² to find 41 × 39.
33. 33.Use (a + b)² = a² + 2ab + b² to find 26².
34. 34.Use (a + b)(a − b) = a² − b² to find 62 × 58.
35. 35.Use (a + b)² = a² + 2ab + b² to find 23².
36. 36.Find the value of x² + 2xy + y² when x = 10 and y = 1.
37. 37.Use (a + b)(a − b) = a² − b² to find 57 × 43.
38. 38.Use (a + b)² = a² + 2ab + b² to find 107².
39. 39.Use a² − b² = (a + b)(a − b) to find 30² − 13².
40. 40.Use (a + b)² = a² + 2ab + b² to find 78².

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