Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 966 · 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.If a − b = 5 and ab = 84, what is a² + b²?
2. 2.If a + b = 9 and ab = 20, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 28² − 4².
4. 4.Use (a + b)(a − b) = a² − b² to find 62 × 58.
5. 5.Use (a + b)(a − b) = a² − b² to find 27 × 13.
6. 6.Use a² − b² = (a + b)(a − b) to find 25² − 14².
7. 7.Use (a − b)² = a² − 2ab + b² to find 52².
8. 8.Find the value of x² − y² when x = 9 and y = 5.
9. 9.Use (a + b)(a − b) = a² − b² to find 37 × 23.
10. 10.Use (a + b)² = a² + 2ab + b² to find 78².
11. 11.Use (a + b)(a − b) = a² − b² to find 31 × 29.
12. 12.If a + b = 17 and ab = 72, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 28².
14. 14.Use (a + b)(a − b) = a² − b² to find 75 × 65.
15. 15.Use (a + b)(a − b) = a² − b² to find 97 × 83.
16. 16.Find the value of x² − y² when x = 15 and y = 1.
17. 17.If a − b = 3 and ab = 28, what is a² + b²?
18. 18.If a − b = 1 and ab = 6, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 40² − 34².
20. 20.If a + b = 15 and ab = 56, what is a² + b²?
21. 21.Find the value of x² + 2xy + y² when x = 13 and y = 2.
22. 22.Find the value of x² + 2xy + y² when x = 7 and y = 5.
23. 23.Use (a + b)² = a² + 2ab + b² to find 46².
24. 24.Use (a + b)(a − b) = a² − b² to find 44 × 36.
25. 25.Use (a + b)² = a² + 2ab + b² to find 48².
26. 26.Use a² − b² = (a + b)(a − b) to find 74² − 15².
27. 27.If a − b = 6 and ab = 40, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 23².
29. 29.Use (a − b)² = a² − 2ab + b² to find 94².
30. 30.Use a² − b² = (a + b)(a − b) to find 43² − 11².
31. 31.Use (a + b)(a − b) = a² − b² to find 22 × 18.
32. 32.Find the value of x² + 2xy + y² when x = 7 and y = 4.
33. 33.Use (a + b)² = a² + 2ab + b² to find 52².
34. 34.Use a² − b² = (a + b)(a − b) to find 42² − 16².
35. 35.Use (a + b)(a − b) = a² − b² to find 84 × 76.
36. 36.Use (a + b)(a − b) = a² − b² to find 55 × 45.
37. 37.Use (a + b)² = a² + 2ab + b² to find 36².
38. 38.Use (a + b)² = a² + 2ab + b² to find 63².
39. 39.Find the value of x² − y² when x = 7 and y = 1.
40. 40.If a + b = 11 and ab = 30, what is a² + b²?

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