Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 584 · 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 41² − 7².
2. 2.Use (a + b)² = a² + 2ab + b² to find 47².
3. 3.Find the value of x² − y² when x = 11 and y = 1.
4. 4.Find the value of x² − 2xy + y² when x = 13 and y = 7.
5. 5.Use (a − b)² = a² − 2ab + b² to find 68².
6. 6.Use a² − b² = (a + b)(a − b) to find 20² − 15².
7. 7.Find the value of x² − y² when x = 4 and y = 3.
8. 8.Use a² − b² = (a + b)(a − b) to find 32² − 24².
9. 9.Use (a + b)² = a² + 2ab + b² to find 95².
10. 10.Use (a + b)(a − b) = a² − b² to find 64 × 56.
11. 11.Find the value of x² + 2xy + y² when x = 12 and y = 2.
12. 12.Use (a + b)² = a² + 2ab + b² to find 63².
13. 13.If a − b = 5 and ab = 24, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 42².
15. 15.Use (a − b)² = a² − 2ab + b² to find 74².
16. 16.Find the value of x² − 2xy + y² when x = 12 and y = 6.
17. 17.Use (a + b)(a − b) = a² − b² to find 23 × 17.
18. 18.Find the value of x² − y² when x = 8 and y = 1.
19. 19.Use (a − b)² = a² − 2ab + b² to find 16².
20. 20.Find the value of x² − y² when x = 10 and y = 6.
21. 21.Find the value of x² + 2xy + y² when x = 3 and y = 2.
22. 22.Use a² − b² = (a + b)(a − b) to find 38² − 29².
23. 23.Use (a + b)(a − b) = a² − b² to find 25 × 15.
24. 24.Use (a − b)² = a² − 2ab + b² to find 53².
25. 25.Find the value of x² + 2xy + y² when x = 13 and y = 7.
26. 26.Use (a + b)² = a² + 2ab + b² to find 88².
27. 27.Use (a + b)² = a² + 2ab + b² to find 72².
28. 28.Use (a − b)² = a² − 2ab + b² to find 35².
29. 29.Find the value of x² − y² when x = 3 and y = 2.
30. 30.Use a² − b² = (a + b)(a − b) to find 37² − 7².
31. 31.Use (a + b)² = a² + 2ab + b² to find 15².
32. 32.Use (a − b)² = a² − 2ab + b² to find 11².
33. 33.Find the value of x² + 2xy + y² when x = 4 and y = 1.
34. 34.Use (a + b)(a − b) = a² − b² to find 84 × 76.
35. 35.Use a² − b² = (a + b)(a − b) to find 91² − 31².
36. 36.Use (a + b)² = a² + 2ab + b² to find 85².
37. 37.Use (a + b)² = a² + 2ab + b² to find 38².
38. 38.Use (a + b)(a − b) = a² − b² to find 62 × 58.
39. 39.If a − b = 1 and ab = 6, what is a² + b²?
40. 40.Find the value of x² − y² when x = 15 and y = 11.

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