Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 112 · 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 = 8 and ab = 7, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 74².
3. 3.Use (a − b)² = a² − 2ab + b² to find 39².
4. 4.If a + b = 17 and ab = 60, what is a² + b²?
5. 5.Find the value of x² − y² when x = 5 and y = 3.
6. 6.If a + b = 15 and ab = 54, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 53².
8. 8.Use (a + b)² = a² + 2ab + b² to find 12².
9. 9.If a + b = 10 and ab = 21, what is a² + b²?
10. 10.Find the value of x² − 2xy + y² when x = 8 and y = 5.
11. 11.Find the value of x² + 2xy + y² when x = 3 and y = 1.
12. 12.If a + b = 8 and ab = 15, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 27 × 13.
14. 14.Find the value of x² − 2xy + y² when x = 5 and y = 4.
15. 15.Use (a + b)² = a² + 2ab + b² to find 79².
16. 16.Find the value of x² − 2xy + y² when x = 11 and y = 3.
17. 17.Find the value of x² − 2xy + y² when x = 13 and y = 1.
18. 18.If a − b = 1 and ab = 132, what is a² + b²?
19. 19.Find the value of x² − y² when x = 13 and y = 7.
20. 20.Use (a + b)(a − b) = a² − b² to find 64 × 56.
21. 21.Use (a + b)² = a² + 2ab + b² to find 54².
22. 22.Find the value of x² − 2xy + y² when x = 6 and y = 5.
23. 23.Find the value of x² + 2xy + y² when x = 13 and y = 9.
24. 24.Use (a − b)² = a² − 2ab + b² to find 13².
25. 25.Find the value of x² − 2xy + y² when x = 9 and y = 1.
26. 26.Use (a − b)² = a² − 2ab + b² to find 55².
27. 27.Use (a + b)(a − b) = a² − b² to find 61 × 59.
28. 28.Use (a − b)² = a² − 2ab + b² to find 58².
29. 29.Use a² − b² = (a + b)(a − b) to find 70² − 6².
30. 30.Use a² − b² = (a + b)(a − b) to find 78² − 68².
31. 31.Use a² − b² = (a + b)(a − b) to find 38² − 30².
32. 32.If a + b = 15 and ab = 36, what is a² + b²?
33. 33.If a + b = 10 and ab = 24, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 84².
35. 35.Use a² − b² = (a + b)(a − b) to find 79² − 11².
36. 36.If a + b = 21 and ab = 110, what is a² + b²?
37. 37.If a + b = 9 and ab = 8, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 99².
39. 39.If a − b = 1 and ab = 72, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 87 × 73.

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