Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 722 · 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 27².
2. 2.Use (a + b)² = a² + 2ab + b² to find 11².
3. 3.Use (a + b)² = a² + 2ab + b² to find 89².
4. 4.Find the value of x² + 2xy + y² when x = 9 and y = 5.
5. 5.If a + b = 13 and ab = 42, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 89².
7. 7.Use (a + b)² = a² + 2ab + b² to find 67².
8. 8.If a − b = 2 and ab = 8, what is a² + b²?
9. 9.Find the value of x² + 2xy + y² when x = 5 and y = 1.
10. 10.Find the value of x² − 2xy + y² when x = 3 and y = 2.
11. 11.Use (a + b)² = a² + 2ab + b² to find 79².
12. 12.If a + b = 7 and ab = 12, what is a² + b²?
13. 13.Find the value of x² − 2xy + y² when x = 4 and y = 3.
14. 14.If a + b = 6 and ab = 8, what is a² + b²?
15. 15.Find the value of x² + 2xy + y² when x = 9 and y = 1.
16. 16.Use a² − b² = (a + b)(a − b) to find 23² − 20².
17. 17.Use (a + b)² = a² + 2ab + b² to find 81².
18. 18.Use (a + b)(a − b) = a² − b² to find 106 × 94.
19. 19.Use (a + b)² = a² + 2ab + b² to find 29².
20. 20.Find the value of x² + 2xy + y² when x = 4 and y = 1.
21. 21.Use a² − b² = (a + b)(a − b) to find 98² − 83².
22. 22.Use a² − b² = (a + b)(a − b) to find 44² − 41².
23. 23.Use (a + b)(a − b) = a² − b² to find 48 × 32.
24. 24.Use a² − b² = (a + b)(a − b) to find 72² − 7².
25. 25.Use (a − b)² = a² − 2ab + b² to find 45².
26. 26.If a − b = 3 and ab = 10, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 73².
28. 28.Find the value of x² + 2xy + y² when x = 15 and y = 11.
29. 29.Use a² − b² = (a + b)(a − b) to find 65² − 47².
30. 30.Find the value of x² + 2xy + y² when x = 10 and y = 6.
31. 31.Use (a − b)² = a² − 2ab + b² to find 68².
32. 32.Find the value of x² + 2xy + y² when x = 3 and y = 2.
33. 33.If a + b = 5 and ab = 4, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 32².
35. 35.Use a² − b² = (a + b)(a − b) to find 81² − 56².
36. 36.Use (a + b)(a − b) = a² − b² to find 79 × 61.
37. 37.Find the value of x² − y² when x = 8 and y = 4.
38. 38.Use (a + b)(a − b) = a² − b² to find 61 × 59.
39. 39.Use (a + b)² = a² + 2ab + b² to find 73².
40. 40.Use (a + b)² = a² + 2ab + b² to find 32².

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