Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 716 · 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 68².
2. 2.Use (a + b)² = a² + 2ab + b² to find 25².
3. 3.If a − b = 1 and ab = 2, what is a² + b²?
4. 4.Find the value of x² + 2xy + y² when x = 13 and y = 5.
5. 5.Use a² − b² = (a + b)(a − b) to find 77² − 32².
6. 6.If a + b = 4 and ab = 3, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 28 × 12.
8. 8.If a + b = 6 and ab = 5, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 58 × 42.
10. 10.Use (a − b)² = a² − 2ab + b² to find 89².
11. 11.Find the value of x² − 2xy + y² when x = 3 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 95² − 6².
13. 13.Use a² − b² = (a + b)(a − b) to find 42² − 11².
14. 14.Find the value of x² − 2xy + y² when x = 5 and y = 1.
15. 15.Use (a + b)² = a² + 2ab + b² to find 72².
16. 16.Use (a − b)² = a² − 2ab + b² to find 48².
17. 17.Use a² − b² = (a + b)(a − b) to find 25² − 15².
18. 18.Find the value of x² − 2xy + y² when x = 4 and y = 3.
19. 19.Use (a + b)² = a² + 2ab + b² to find 33².
20. 20.Use (a + b)(a − b) = a² − b² to find 102 × 98.
21. 21.If a + b = 6 and ab = 8, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 101².
23. 23.Use a² − b² = (a + b)(a − b) to find 39² − 22².
24. 24.If a − b = 4 and ab = 12, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 93².
26. 26.Use (a + b)² = a² + 2ab + b² to find 29².
27. 27.Use a² − b² = (a + b)(a − b) to find 47² − 4².
28. 28.If a − b = 3 and ab = 70, what is a² + b²?
29. 29.Find the value of x² + 2xy + y² when x = 13 and y = 12.
30. 30.Find the value of x² + 2xy + y² when x = 3 and y = 1.
31. 31.Use (a + b)(a − b) = a² − b² to find 105 × 95.
32. 32.Find the value of x² + 2xy + y² when x = 9 and y = 5.
33. 33.If a − b = 7 and ab = 44, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 61 × 59.
35. 35.Use a² − b² = (a + b)(a − b) to find 20² − 8².
36. 36.Use (a − b)² = a² − 2ab + b² to find 95².
37. 37.Use (a − b)² = a² − 2ab + b² to find 34².
38. 38.Use (a + b)² = a² + 2ab + b² to find 28².
39. 39.Use (a + b)(a − b) = a² − b² to find 87 × 73.
40. 40.Use (a − b)² = a² − 2ab + b² to find 32².

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