Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 591 · 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 71².
2. 2.Use (a + b)(a − b) = a² − b² to find 47 × 33.
3. 3.Use (a + b)(a − b) = a² − b² to find 77 × 63.
4. 4.Use (a − b)² = a² − 2ab + b² to find 72².
5. 5.Find the value of x² − y² when x = 10 and y = 9.
6. 6.Use a² − b² = (a + b)(a − b) to find 53² − 9².
7. 7.Use (a + b)(a − b) = a² − b² to find 48 × 32.
8. 8.Use (a − b)² = a² − 2ab + b² to find 42².
9. 9.Use (a + b)(a − b) = a² − b² to find 104 × 96.
10. 10.If a + b = 21 and ab = 110, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 22² − 19².
12. 12.Find the value of x² − 2xy + y² when x = 9 and y = 5.
13. 13.Use (a + b)(a − b) = a² − b² to find 45 × 35.
14. 14.Use (a + b)(a − b) = a² − b² to find 27 × 13.
15. 15.Use (a + b)² = a² + 2ab + b² to find 11².
16. 16.Find the value of x² + 2xy + y² when x = 9 and y = 4.
17. 17.Use (a − b)² = a² − 2ab + b² to find 15².
18. 18.Use a² − b² = (a + b)(a − b) to find 27² − 15².
19. 19.Use (a − b)² = a² − 2ab + b² to find 78².
20. 20.Use a² − b² = (a + b)(a − b) to find 35² − 5².
21. 21.Use (a − b)² = a² − 2ab + b² to find 54².
22. 22.Use (a + b)(a − b) = a² − b² to find 31 × 29.
23. 23.Use (a + b)² = a² + 2ab + b² to find 23².
24. 24.If a + b = 7 and ab = 10, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 21² − 7².
26. 26.If a − b = 1 and ab = 42, what is a² + b²?
27. 27.Find the value of x² + 2xy + y² when x = 15 and y = 14.
28. 28.Find the value of x² − y² when x = 10 and y = 3.
29. 29.Use (a + b)² = a² + 2ab + b² to find 72².
30. 30.Use (a + b)² = a² + 2ab + b² to find 96².
31. 31.Use (a − b)² = a² − 2ab + b² to find 88².
32. 32.Use (a + b)² = a² + 2ab + b² to find 44².
33. 33.Use (a − b)² = a² − 2ab + b² to find 69².
34. 34.If a − b = 1 and ab = 132, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 42 × 38.
36. 36.Use a² − b² = (a + b)(a − b) to find 70² − 17².
37. 37.Use a² − b² = (a + b)(a − b) to find 89² − 11².
38. 38.Use (a − b)² = a² − 2ab + b² to find 46².
39. 39.Use (a + b)(a − b) = a² − b² to find 25 × 15.
40. 40.Use (a − b)² = a² − 2ab + b² to find 61².

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