Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 418 · 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 39² − 4².
2. 2.If a − b = 6 and ab = 27, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 55².
4. 4.If a − b = 2 and ab = 48, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 101².
6. 6.Use (a + b)² = a² + 2ab + b² to find 79².
7. 7.If a + b = 3 and ab = 2, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 23².
9. 9.Use (a + b)² = a² + 2ab + b² to find 85².
10. 10.If a − b = 1 and ab = 30, what is a² + b²?
11. 11.If a − b = 1 and ab = 72, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 50² − 9².
13. 13.Use a² − b² = (a + b)(a − b) to find 48² − 37².
14. 14.Use (a + b)(a − b) = a² − b² to find 101 × 99.
15. 15.Use a² − b² = (a + b)(a − b) to find 75² − 6².
16. 16.If a + b = 8 and ab = 12, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 62².
18. 18.Find the value of x² + 2xy + y² when x = 4 and y = 3.
19. 19.Use (a + b)(a − b) = a² − b² to find 84 × 76.
20. 20.Find the value of x² + 2xy + y² when x = 12 and y = 7.
21. 21.If a + b = 17 and ab = 72, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 86² − 52².
23. 23.Use (a + b)² = a² + 2ab + b² to find 57².
24. 24.If a − b = 4 and ab = 5, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 65².
26. 26.Use a² − b² = (a + b)(a − b) to find 35² − 7².
27. 27.Use (a − b)² = a² − 2ab + b² to find 84².
28. 28.Use (a + b)² = a² + 2ab + b² to find 21².
29. 29.Use (a + b)² = a² + 2ab + b² to find 42².
30. 30.Use (a − b)² = a² − 2ab + b² to find 39².
31. 31.Use (a + b)² = a² + 2ab + b² to find 25².
32. 32.Use (a + b)² = a² + 2ab + b² to find 37².
33. 33.Find the value of x² + 2xy + y² when x = 8 and y = 5.
34. 34.Use (a − b)² = a² − 2ab + b² to find 53².
35. 35.Find the value of x² + 2xy + y² when x = 10 and y = 9.
36. 36.Use (a − b)² = a² − 2ab + b² to find 88².
37. 37.Use a² − b² = (a + b)(a − b) to find 31² − 3².
38. 38.Use (a + b)² = a² + 2ab + b² to find 22².
39. 39.If a + b = 15 and ab = 56, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 72².

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