Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 751 · 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 = 14 and ab = 24, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 72² − 2².
3. 3.Use (a + b)² = a² + 2ab + b² to find 61².
4. 4.Use (a + b)(a − b) = a² − b² to find 89 × 71.
5. 5.Use (a − b)² = a² − 2ab + b² to find 59².
6. 6.Use (a − b)² = a² − 2ab + b² to find 84².
7. 7.If a − b = 3 and ab = 40, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 36².
9. 9.Find the value of x² − y² when x = 11 and y = 7.
10. 10.Use (a + b)² = a² + 2ab + b² to find 64².
11. 11.Find the value of x² + 2xy + y² when x = 13 and y = 10.
12. 12.Use a² − b² = (a + b)(a − b) to find 58² − 7².
13. 13.If a − b = 6 and ab = 55, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 38².
15. 15.Use a² − b² = (a + b)(a − b) to find 36² − 24².
16. 16.Use (a + b)² = a² + 2ab + b² to find 84².
17. 17.Use a² − b² = (a + b)(a − b) to find 81² − 32².
18. 18.Use (a + b)(a − b) = a² − b² to find 88 × 72.
19. 19.Find the value of x² + 2xy + y² when x = 3 and y = 1.
20. 20.Find the value of x² − 2xy + y² when x = 12 and y = 6.
21. 21.Use (a + b)² = a² + 2ab + b² to find 52².
22. 22.Use (a + b)(a − b) = a² − b² to find 42 × 38.
23. 23.If a + b = 6 and ab = 5, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 49².
25. 25.Use (a + b)² = a² + 2ab + b² to find 28².
26. 26.Find the value of x² + 2xy + y² when x = 3 and y = 2.
27. 27.Use (a + b)² = a² + 2ab + b² to find 25².
28. 28.Use (a + b)² = a² + 2ab + b² to find 21².
29. 29.Find the value of x² − 2xy + y² when x = 10 and y = 9.
30. 30.Find the value of x² + 2xy + y² when x = 14 and y = 8.
31. 31.Use a² − b² = (a + b)(a − b) to find 71² − 19².
32. 32.If a + b = 7 and ab = 12, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 43 × 37.
34. 34.Use a² − b² = (a + b)(a − b) to find 83² − 48².
35. 35.Use (a + b)(a − b) = a² − b² to find 73 × 67.
36. 36.If a − b = 1 and ab = 2, what is a² + b²?
37. 37.Find the value of x² − y² when x = 6 and y = 2.
38. 38.Find the value of x² − y² when x = 14 and y = 9.
39. 39.Use (a − b)² = a² − 2ab + b² to find 68².
40. 40.Use (a + b)(a − b) = a² − b² to find 72 × 68.

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