Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 340 · 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 = 5 and y = 2.
2. 2.Use (a + b)(a − b) = a² − b² to find 78 × 62.
3. 3.Use a² − b² = (a + b)(a − b) to find 42² − 37².
4. 4.If a − b = 3 and ab = 18, what is a² + b²?
5. 5.If a + b = 11 and ab = 18, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 95².
7. 7.If a + b = 9 and ab = 14, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 99².
9. 9.Use (a − b)² = a² − 2ab + b² to find 31².
10. 10.Use (a + b)² = a² + 2ab + b² to find 84².
11. 11.Use a² − b² = (a + b)(a − b) to find 37² − 20².
12. 12.Find the value of x² − 2xy + y² when x = 15 and y = 2.
13. 13.Find the value of x² − 2xy + y² when x = 6 and y = 1.
14. 14.If a − b = 2 and ab = 15, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 104².
16. 16.Use (a + b)² = a² + 2ab + b² to find 75².
17. 17.Use (a + b)² = a² + 2ab + b² to find 73².
18. 18.Find the value of x² + 2xy + y² when x = 12 and y = 11.
19. 19.Use (a − b)² = a² − 2ab + b² to find 37².
20. 20.Use a² − b² = (a + b)(a − b) to find 38² − 7².
21. 21.Find the value of x² − y² when x = 6 and y = 1.
22. 22.Use a² − b² = (a + b)(a − b) to find 45² − 44².
23. 23.Use a² − b² = (a + b)(a − b) to find 82² − 36².
24. 24.Use (a − b)² = a² − 2ab + b² to find 68².
25. 25.Find the value of x² − 2xy + y² when x = 5 and y = 4.
26. 26.Use (a + b)(a − b) = a² − b² to find 96 × 84.
27. 27.Use (a + b)(a − b) = a² − b² to find 69 × 51.
28. 28.Use (a − b)² = a² − 2ab + b² to find 64².
29. 29.If a + b = 8 and ab = 7, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 43².
31. 31.Use (a + b)(a − b) = a² − b² to find 34 × 26.
32. 32.Use (a + b)² = a² + 2ab + b² to find 107².
33. 33.Find the value of x² − 2xy + y² when x = 10 and y = 8.
34. 34.Find the value of x² + 2xy + y² when x = 8 and y = 3.
35. 35.Use (a − b)² = a² − 2ab + b² to find 93².
36. 36.If a + b = 13 and ab = 36, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 62² − 37².
38. 38.Use (a + b)(a − b) = a² − b² to find 101 × 99.
39. 39.Find the value of x² + 2xy + y² when x = 8 and y = 7.
40. 40.Use (a + b)² = a² + 2ab + b² to find 16².

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