Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 345 · 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)² = a² + 2ab + b² to find 35².
2. 2.Use (a + b)² = a² + 2ab + b² to find 47².
3. 3.Use (a − b)² = a² − 2ab + b² to find 36².
4. 4.If a + b = 15 and ab = 54, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 39².
6. 6.Use (a + b)² = a² + 2ab + b² to find 55².
7. 7.Use (a + b)² = a² + 2ab + b² to find 34².
8. 8.Find the value of x² − y² when x = 15 and y = 9.
9. 9.Use a² − b² = (a + b)(a − b) to find 42² − 32².
10. 10.Use (a + b)² = a² + 2ab + b² to find 22².
11. 11.Use (a − b)² = a² − 2ab + b² to find 39².
12. 12.Use (a − b)² = a² − 2ab + b² to find 43².
13. 13.Use (a + b)(a − b) = a² − b² to find 52 × 48.
14. 14.Use (a − b)² = a² − 2ab + b² to find 24².
15. 15.Use (a + b)(a − b) = a² − b² to find 32 × 28.
16. 16.If a + b = 11 and ab = 10, what is a² + b²?
17. 17.If a + b = 6 and ab = 8, what is a² + b²?
18. 18.Find the value of x² − y² when x = 3 and y = 1.
19. 19.Use a² − b² = (a + b)(a − b) to find 60² − 38².
20. 20.Use a² − b² = (a + b)(a − b) to find 74² − 1².
21. 21.Use (a + b)(a − b) = a² − b² to find 69 × 51.
22. 22.If a + b = 9 and ab = 14, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 16².
24. 24.Use (a − b)² = a² − 2ab + b² to find 82².
25. 25.Use (a + b)² = a² + 2ab + b² to find 67².
26. 26.Use (a − b)² = a² − 2ab + b² to find 67².
27. 27.Use a² − b² = (a + b)(a − b) to find 44² − 39².
28. 28.Use (a + b)² = a² + 2ab + b² to find 92².
29. 29.Find the value of x² − 2xy + y² when x = 13 and y = 9.
30. 30.Use (a − b)² = a² − 2ab + b² to find 92².
31. 31.Use (a + b)² = a² + 2ab + b² to find 15².
32. 32.Find the value of x² − y² when x = 7 and y = 6.
33. 33.Use a² − b² = (a + b)(a − b) to find 72² − 14².
34. 34.Use (a + b)(a − b) = a² − b² to find 74 × 66.
35. 35.Find the value of x² + 2xy + y² when x = 4 and y = 2.
36. 36.If a − b = 1 and ab = 56, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 24² − 11².
38. 38.Use a² − b² = (a + b)(a − b) to find 74² − 57².
39. 39.Use (a − b)² = a² − 2ab + b² to find 99².
40. 40.Use (a + b)² = a² + 2ab + b² to find 38².

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