Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 507 · 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.Find the value of x² − 2xy + y² when x = 14 and y = 8.
2. 2.Use (a + b)(a − b) = a² − b² to find 101 × 99.
3. 3.If a + b = 5 and ab = 4, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 82 × 78.
5. 5.Find the value of x² − y² when x = 8 and y = 6.
6. 6.Use (a + b)² = a² + 2ab + b² to find 47².
7. 7.Use (a + b)(a − b) = a² − b² to find 51 × 49.
8. 8.Use (a + b)(a − b) = a² − b² to find 64 × 56.
9. 9.Use (a − b)² = a² − 2ab + b² to find 28².
10. 10.If a + b = 21 and ab = 108, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 34 × 26.
12. 12.Use (a + b)(a − b) = a² − b² to find 56 × 44.
13. 13.Use a² − b² = (a + b)(a − b) to find 92² − 70².
14. 14.If a + b = 13 and ab = 42, what is a² + b²?
15. 15.Find the value of x² − 2xy + y² when x = 14 and y = 6.
16. 16.Use (a + b)(a − b) = a² − b² to find 27 × 13.
17. 17.Use (a + b)(a − b) = a² − b² to find 33 × 27.
18. 18.Find the value of x² + 2xy + y² when x = 5 and y = 1.
19. 19.Find the value of x² + 2xy + y² when x = 5 and y = 4.
20. 20.Find the value of x² + 2xy + y² when x = 15 and y = 3.
21. 21.Use (a − b)² = a² − 2ab + b² to find 31².
22. 22.If a + b = 17 and ab = 66, what is a² + b²?
23. 23.Find the value of x² − 2xy + y² when x = 10 and y = 2.
24. 24.Find the value of x² − y² when x = 13 and y = 10.
25. 25.Find the value of x² + 2xy + y² when x = 13 and y = 12.
26. 26.Use (a + b)(a − b) = a² − b² to find 35 × 25.
27. 27.Use a² − b² = (a + b)(a − b) to find 29² − 23².
28. 28.Find the value of x² − 2xy + y² when x = 7 and y = 2.
29. 29.Use (a + b)² = a² + 2ab + b² to find 91².
30. 30.Use (a + b)(a − b) = a² − b² to find 73 × 67.
31. 31.Use (a + b)² = a² + 2ab + b² to find 75².
32. 32.Find the value of x² − y² when x = 6 and y = 2.
33. 33.If a + b = 6 and ab = 5, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 69 × 51.
35. 35.Find the value of x² + 2xy + y² when x = 4 and y = 3.
36. 36.If a − b = 3 and ab = 4, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 24² − 1².
38. 38.Use (a − b)² = a² − 2ab + b² to find 86².
39. 39.Use (a + b)(a − b) = a² − b² to find 53 × 47.
40. 40.Use (a + b)² = a² + 2ab + b² to find 46².

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