Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 768 · 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 79².
2. 2.Use a² − b² = (a + b)(a − b) to find 85² − 60².
3. 3.Use (a − b)² = a² − 2ab + b² to find 94².
4. 4.Find the value of x² + 2xy + y² when x = 8 and y = 7.
5. 5.If a − b = 4 and ab = 5, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 67².
7. 7.Use a² − b² = (a + b)(a − b) to find 49² − 11².
8. 8.Use (a − b)² = a² − 2ab + b² to find 83².
9. 9.Use (a + b)² = a² + 2ab + b² to find 37².
10. 10.Find the value of x² − y² when x = 15 and y = 1.
11. 11.Use (a − b)² = a² − 2ab + b² to find 42².
12. 12.Find the value of x² − y² when x = 10 and y = 3.
13. 13.Use (a + b)(a − b) = a² − b² to find 49 × 31.
14. 14.If a − b = 2 and ab = 3, what is a² + b²?
15. 15.Find the value of x² − 2xy + y² when x = 7 and y = 1.
16. 16.Find the value of x² − y² when x = 13 and y = 12.
17. 17.Use (a + b)(a − b) = a² − b² to find 87 × 73.
18. 18.Use (a − b)² = a² − 2ab + b² to find 68².
19. 19.Use (a + b)(a − b) = a² − b² to find 88 × 72.
20. 20.Use (a + b)² = a² + 2ab + b² to find 78².
21. 21.Use (a + b)² = a² + 2ab + b² to find 49².
22. 22.Use a² − b² = (a + b)(a − b) to find 92² − 8².
23. 23.Use (a − b)² = a² − 2ab + b² to find 39².
24. 24.Use a² − b² = (a + b)(a − b) to find 86² − 32².
25. 25.Use (a + b)² = a² + 2ab + b² to find 72².
26. 26.Use (a − b)² = a² − 2ab + b² to find 43².
27. 27.If a − b = 1 and ab = 12, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 93 × 87.
29. 29.If a + b = 19 and ab = 90, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 79² − 52².
31. 31.Use (a + b)² = a² + 2ab + b² to find 17².
32. 32.Use a² − b² = (a + b)(a − b) to find 65² − 43².
33. 33.Use (a + b)(a − b) = a² − b² to find 32 × 28.
34. 34.Use (a − b)² = a² − 2ab + b² to find 26².
35. 35.If a + b = 16 and ab = 48, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 81².
37. 37.Find the value of x² − 2xy + y² when x = 6 and y = 3.
38. 38.If a − b = 7 and ab = 44, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 25² − 19².
40. 40.If a + b = 10 and ab = 24, what is a² + b²?

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