Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 516 · 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)(a − b) = a² − b² to find 32 × 28.
2. 2.Use a² − b² = (a + b)(a − b) to find 36² − 31².
3. 3.Use (a + b)² = a² + 2ab + b² to find 64².
4. 4.Find the value of x² + 2xy + y² when x = 5 and y = 4.
5. 5.Use (a + b)(a − b) = a² − b² to find 79 × 61.
6. 6.Use (a + b)(a − b) = a² − b² to find 72 × 68.
7. 7.Find the value of x² − 2xy + y² when x = 10 and y = 3.
8. 8.Find the value of x² − y² when x = 10 and y = 4.
9. 9.If a + b = 4 and ab = 3, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 26².
11. 11.Use (a − b)² = a² − 2ab + b² to find 77².
12. 12.Use a² − b² = (a + b)(a − b) to find 34² − 18².
13. 13.Find the value of x² + 2xy + y² when x = 6 and y = 4.
14. 14.If a − b = 9 and ab = 36, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 21².
16. 16.Use (a − b)² = a² − 2ab + b² to find 81².
17. 17.Use (a − b)² = a² − 2ab + b² to find 41².
18. 18.Use (a − b)² = a² − 2ab + b² to find 32².
19. 19.Use a² − b² = (a + b)(a − b) to find 68² − 43².
20. 20.Use (a + b)(a − b) = a² − b² to find 23 × 17.
21. 21.Use a² − b² = (a + b)(a − b) to find 74² − 67².
22. 22.Find the value of x² − y² when x = 5 and y = 1.
23. 23.Use (a + b)(a − b) = a² − b² to find 34 × 26.
24. 24.If a − b = 6 and ab = 40, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 46².
26. 26.Use (a − b)² = a² − 2ab + b² to find 72².
27. 27.Use (a + b)(a − b) = a² − b² to find 108 × 92.
28. 28.Use a² − b² = (a + b)(a − b) to find 23² − 9².
29. 29.Use (a − b)² = a² − 2ab + b² to find 61².
30. 30.Find the value of x² − 2xy + y² when x = 13 and y = 8.
31. 31.Find the value of x² + 2xy + y² when x = 15 and y = 4.
32. 32.If a + b = 3 and ab = 2, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 19².
34. 34.If a + b = 16 and ab = 63, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 86 × 74.
36. 36.Use (a + b)² = a² + 2ab + b² to find 94².
37. 37.Find the value of x² + 2xy + y² when x = 14 and y = 4.
38. 38.Use (a − b)² = a² − 2ab + b² to find 21².
39. 39.If a + b = 10 and ab = 16, what is a² + b²?
40. 40.If a + b = 8 and ab = 12, what is a² + b²?

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