Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 931 · 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 26² − 21².
2. 2.Find the value of x² − y² when x = 15 and y = 9.
3. 3.Find the value of x² − 2xy + y² when x = 14 and y = 7.
4. 4.Use a² − b² = (a + b)(a − b) to find 30² − 8².
5. 5.Use (a + b)² = a² + 2ab + b² to find 29².
6. 6.Use (a + b)² = a² + 2ab + b² to find 58².
7. 7.Use (a − b)² = a² − 2ab + b² to find 26².
8. 8.Use (a − b)² = a² − 2ab + b² to find 16².
9. 9.Use (a + b)² = a² + 2ab + b² to find 66².
10. 10.Use (a + b)(a − b) = a² − b² to find 102 × 98.
11. 11.Use a² − b² = (a + b)(a − b) to find 47² − 32².
12. 12.Use a² − b² = (a + b)(a − b) to find 86² − 8².
13. 13.If a − b = 4 and ab = 45, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 65².
15. 15.Use (a + b)(a − b) = a² − b² to find 72 × 68.
16. 16.Use (a + b)² = a² + 2ab + b² to find 72².
17. 17.Use (a − b)² = a² − 2ab + b² to find 33².
18. 18.Use a² − b² = (a + b)(a − b) to find 41² − 30².
19. 19.Use (a − b)² = a² − 2ab + b² to find 84².
20. 20.Use (a + b)(a − b) = a² − b² to find 48 × 32.
21. 21.If a + b = 18 and ab = 77, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 45 × 35.
23. 23.Find the value of x² + 2xy + y² when x = 10 and y = 3.
24. 24.Find the value of x² − y² when x = 11 and y = 3.
25. 25.Find the value of x² − y² when x = 12 and y = 5.
26. 26.Use a² − b² = (a + b)(a − b) to find 20² − 10².
27. 27.If a + b = 6 and ab = 5, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 25² − 7².
29. 29.Find the value of x² + 2xy + y² when x = 6 and y = 4.
30. 30.If a − b = 6 and ab = 27, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 103².
32. 32.Use (a − b)² = a² − 2ab + b² to find 15².
33. 33.Use (a + b)² = a² + 2ab + b² to find 109².
34. 34.Use a² − b² = (a + b)(a − b) to find 21² − 6².
35. 35.Use (a − b)² = a² − 2ab + b² to find 78².
36. 36.Use (a + b)² = a² + 2ab + b² to find 11².
37. 37.Use (a + b)(a − b) = a² − b² to find 41 × 39.
38. 38.If a − b = 9 and ab = 36, what is a² + b²?
39. 39.If a + b = 3 and ab = 2, what is a² + b²?
40. 40.Find the value of x² − y² when x = 7 and y = 5.

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