Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 511 · 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 74².
2. 2.Find the value of x² + 2xy + y² when x = 12 and y = 2.
3. 3.Use a² − b² = (a + b)(a − b) to find 73² − 37².
4. 4.Find the value of x² + 2xy + y² when x = 8 and y = 5.
5. 5.Use (a − b)² = a² − 2ab + b² to find 99².
6. 6.Use (a + b)² = a² + 2ab + b² to find 37².
7. 7.Use a² − b² = (a + b)(a − b) to find 34² − 11².
8. 8.Use (a + b)² = a² + 2ab + b² to find 46².
9. 9.Use (a + b)(a − b) = a² − b² to find 109 × 91.
10. 10.Use (a − b)² = a² − 2ab + b² to find 88².
11. 11.Use (a + b)(a − b) = a² − b² to find 32 × 28.
12. 12.If a + b = 3 and ab = 2, what is a² + b²?
13. 13.If a − b = 4 and ab = 5, what is a² + b²?
14. 14.Find the value of x² − 2xy + y² when x = 13 and y = 9.
15. 15.Find the value of x² − 2xy + y² when x = 6 and y = 3.
16. 16.Use (a + b)(a − b) = a² − b² to find 64 × 56.
17. 17.If a − b = 5 and ab = 14, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 92 × 88.
19. 19.Use a² − b² = (a + b)(a − b) to find 85² − 37².
20. 20.Use (a + b)² = a² + 2ab + b² to find 73².
21. 21.Use a² − b² = (a + b)(a − b) to find 23² − 11².
22. 22.Use (a − b)² = a² − 2ab + b² to find 63².
23. 23.Use a² − b² = (a + b)(a − b) to find 91² − 78².
24. 24.If a − b = 4 and ab = 12, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 32².
26. 26.If a + b = 9 and ab = 18, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 44².
28. 28.Use a² − b² = (a + b)(a − b) to find 43² − 24².
29. 29.Use (a + b)² = a² + 2ab + b² to find 17².
30. 30.If a + b = 10 and ab = 16, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 36².
32. 32.Use (a + b)² = a² + 2ab + b² to find 62².
33. 33.Use (a + b)(a − b) = a² − b² to find 21 × 19.
34. 34.Use (a + b)(a − b) = a² − b² to find 86 × 74.
35. 35.If a − b = 6 and ab = 72, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 103².
37. 37.Find the value of x² + 2xy + y² when x = 11 and y = 6.
38. 38.If a + b = 12 and ab = 32, what is a² + b²?
39. 39.Find the value of x² − y² when x = 14 and y = 1.
40. 40.Find the value of x² + 2xy + y² when x = 3 and y = 2.

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