Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 212 · 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)(a − b) = a² − b² to find 53 × 47.
2. 2.Find the value of x² − y² when x = 9 and y = 8.
3. 3.Use a² − b² = (a + b)(a − b) to find 56² − 28².
4. 4.If a + b = 4 and ab = 3, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 4 and y = 1.
6. 6.Use (a − b)² = a² − 2ab + b² to find 33².
7. 7.Use (a + b)² = a² + 2ab + b² to find 73².
8. 8.Use (a − b)² = a² − 2ab + b² to find 97².
9. 9.Find the value of x² − y² when x = 13 and y = 4.
10. 10.Use (a + b)(a − b) = a² − b² to find 69 × 51.
11. 11.Use (a − b)² = a² − 2ab + b² to find 99².
12. 12.Use (a + b)² = a² + 2ab + b² to find 95².
13. 13.Find the value of x² − y² when x = 5 and y = 4.
14. 14.Use (a + b)² = a² + 2ab + b² to find 33².
15. 15.Use a² − b² = (a + b)(a − b) to find 97² − 75².
16. 16.Use (a + b)(a − b) = a² − b² to find 85 × 75.
17. 17.Use (a − b)² = a² − 2ab + b² to find 39².
18. 18.Use (a − b)² = a² − 2ab + b² to find 67².
19. 19.Use (a + b)² = a² + 2ab + b² to find 34².
20. 20.Use (a + b)² = a² + 2ab + b² to find 32².
21. 21.If a + b = 17 and ab = 70, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 98².
23. 23.Use (a − b)² = a² − 2ab + b² to find 15².
24. 24.Use (a − b)² = a² − 2ab + b² to find 28².
25. 25.If a + b = 22 and ab = 120, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 25² − 21².
27. 27.If a + b = 13 and ab = 42, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 47².
29. 29.If a + b = 16 and ab = 48, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 104 × 96.
31. 31.Find the value of x² − y² when x = 3 and y = 2.
32. 32.Use a² − b² = (a + b)(a − b) to find 68² − 38².
33. 33.Use (a + b)(a − b) = a² − b² to find 45 × 35.
34. 34.Use (a + b)² = a² + 2ab + b² to find 87².
35. 35.If a − b = 4 and ab = 5, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 74².
37. 37.Use a² − b² = (a + b)(a − b) to find 77² − 68².
38. 38.Use (a + b)(a − b) = a² − b² to find 79 × 61.
39. 39.Use (a − b)² = a² − 2ab + b² to find 43².
40. 40.Use a² − b² = (a + b)(a − b) to find 21² − 6².

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