Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 259 · 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 31².
2. 2.Use (a + b)² = a² + 2ab + b² to find 47².
3. 3.Use a² − b² = (a + b)(a − b) to find 55² − 32².
4. 4.Use (a + b)(a − b) = a² − b² to find 22 × 18.
5. 5.Use (a + b)(a − b) = a² − b² to find 67 × 53.
6. 6.Use (a + b)² = a² + 2ab + b² to find 16².
7. 7.Use (a − b)² = a² − 2ab + b² to find 42².
8. 8.Use (a + b)(a − b) = a² − b² to find 106 × 94.
9. 9.Use (a + b)(a − b) = a² − b² to find 82 × 78.
10. 10.If a − b = 8 and ab = 20, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 81².
12. 12.Use (a + b)² = a² + 2ab + b² to find 74².
13. 13.Use (a − b)² = a² − 2ab + b² to find 27².
14. 14.Find the value of x² − y² when x = 4 and y = 3.
15. 15.Use (a − b)² = a² − 2ab + b² to find 44².
16. 16.Use (a + b)² = a² + 2ab + b² to find 93².
17. 17.Find the value of x² − y² when x = 8 and y = 7.
18. 18.Use (a + b)² = a² + 2ab + b² to find 38².
19. 19.Find the value of x² + 2xy + y² when x = 10 and y = 2.
20. 20.If a + b = 5 and ab = 6, what is a² + b²?
21. 21.If a + b = 15 and ab = 54, what is a² + b²?
22. 22.If a + b = 13 and ab = 22, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 57² − 36².
24. 24.Use (a − b)² = a² − 2ab + b² to find 78².
25. 25.Use (a − b)² = a² − 2ab + b² to find 98².
26. 26.Use (a + b)(a − b) = a² − b² to find 108 × 92.
27. 27.If a + b = 11 and ab = 30, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 86² − 1².
29. 29.Use a² − b² = (a + b)(a − b) to find 97² − 51².
30. 30.Use (a − b)² = a² − 2ab + b² to find 52².
31. 31.Find the value of x² − y² when x = 10 and y = 3.
32. 32.Use (a + b)(a − b) = a² − b² to find 29 × 11.
33. 33.If a − b = 2 and ab = 8, what is a² + b²?
34. 34.Find the value of x² − y² when x = 7 and y = 2.
35. 35.Find the value of x² + 2xy + y² when x = 10 and y = 1.
36. 36.Use a² − b² = (a + b)(a − b) to find 34² − 17².
37. 37.Use (a − b)² = a² − 2ab + b² to find 63².
38. 38.Use (a + b)² = a² + 2ab + b² to find 104².
39. 39.If a − b = 8 and ab = 9, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 92² − 61².

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