Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 851 · 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.Find the value of x² + 2xy + y² when x = 15 and y = 14.
2. 2.If a + b = 7 and ab = 6, what is a² + b²?
3. 3.Find the value of x² + 2xy + y² when x = 6 and y = 1.
4. 4.Use (a − b)² = a² − 2ab + b² to find 79².
5. 5.Find the value of x² − y² when x = 12 and y = 3.
6. 6.Use (a + b)(a − b) = a² − b² to find 108 × 92.
7. 7.Find the value of x² − 2xy + y² when x = 14 and y = 8.
8. 8.If a − b = 1 and ab = 72, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 23 × 17.
10. 10.Use (a + b)(a − b) = a² − b² to find 72 × 68.
11. 11.Use (a + b)² = a² + 2ab + b² to find 22².
12. 12.Use (a + b)(a − b) = a² − b² to find 34 × 26.
13. 13.Use (a + b)² = a² + 2ab + b² to find 54².
14. 14.Use a² − b² = (a + b)(a − b) to find 43² − 4².
15. 15.Use (a + b)(a − b) = a² − b² to find 44 × 36.
16. 16.If a + b = 5 and ab = 4, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 98² − 65².
18. 18.If a + b = 20 and ab = 96, what is a² + b²?
19. 19.If a − b = 2 and ab = 35, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 88².
21. 21.If a − b = 2 and ab = 3, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 63².
23. 23.If a + b = 4 and ab = 3, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 82 × 78.
25. 25.Use a² − b² = (a + b)(a − b) to find 76² − 49².
26. 26.Use a² − b² = (a + b)(a − b) to find 27² − 24².
27. 27.Use a² − b² = (a + b)(a − b) to find 43² − 17².
28. 28.If a − b = 1 and ab = 56, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 29².
30. 30.Find the value of x² − 2xy + y² when x = 10 and y = 1.
31. 31.Use (a + b)² = a² + 2ab + b² to find 17².
32. 32.If a + b = 3 and ab = 2, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 65².
34. 34.If a + b = 12 and ab = 27, what is a² + b²?
35. 35.Find the value of x² − y² when x = 14 and y = 9.
36. 36.Use (a − b)² = a² − 2ab + b² to find 29².
37. 37.Use a² − b² = (a + b)(a − b) to find 24² − 16².
38. 38.Use (a − b)² = a² − 2ab + b² to find 87².
39. 39.Find the value of x² + 2xy + y² when x = 4 and y = 3.
40. 40.Use (a + b)(a − b) = a² − b² to find 56 × 44.

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