Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 207 · 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.If a + b = 9 and ab = 18, what is a² + b²?
2. 2.If a + b = 10 and ab = 21, what is a² + b²?
3. 3.Find the value of x² + 2xy + y² when x = 4 and y = 1.
4. 4.If a − b = 1 and ab = 2, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 86 × 74.
6. 6.Find the value of x² − 2xy + y² when x = 4 and y = 2.
7. 7.Use (a + b)(a − b) = a² − b² to find 84 × 76.
8. 8.Use (a + b)² = a² + 2ab + b² to find 94².
9. 9.Use a² − b² = (a + b)(a − b) to find 51² − 32².
10. 10.Find the value of x² + 2xy + y² when x = 14 and y = 5.
11. 11.Use (a + b)(a − b) = a² − b² to find 44 × 36.
12. 12.Use (a − b)² = a² − 2ab + b² to find 14².
13. 13.Use (a + b)(a − b) = a² − b² to find 75 × 65.
14. 14.Find the value of x² − y² when x = 12 and y = 3.
15. 15.Use a² − b² = (a + b)(a − b) to find 24² − 22².
16. 16.Use a² − b² = (a + b)(a − b) to find 78² − 67².
17. 17.Find the value of x² − y² when x = 3 and y = 2.
18. 18.Find the value of x² − y² when x = 8 and y = 2.
19. 19.If a − b = 1 and ab = 30, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 76² − 15².
21. 21.Use (a + b)(a − b) = a² − b² to find 55 × 45.
22. 22.Use (a + b)² = a² + 2ab + b² to find 89².
23. 23.If a + b = 14 and ab = 48, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 38².
25. 25.Use (a − b)² = a² − 2ab + b² to find 49².
26. 26.Use (a − b)² = a² − 2ab + b² to find 46².
27. 27.Use a² − b² = (a + b)(a − b) to find 33² − 8².
28. 28.Use (a + b)² = a² + 2ab + b² to find 61².
29. 29.Use a² − b² = (a + b)(a − b) to find 69² − 33².
30. 30.Use (a + b)² = a² + 2ab + b² to find 16².
31. 31.Find the value of x² + 2xy + y² when x = 13 and y = 7.
32. 32.Find the value of x² − y² when x = 11 and y = 2.
33. 33.Use (a − b)² = a² − 2ab + b² to find 43².
34. 34.Use (a + b)(a − b) = a² − b² to find 45 × 35.
35. 35.Use (a + b)(a − b) = a² − b² to find 46 × 34.
36. 36.Use a² − b² = (a + b)(a − b) to find 41² − 2².
37. 37.Use (a + b)(a − b) = a² − b² to find 69 × 51.
38. 38.Use (a − b)² = a² − 2ab + b² to find 51².
39. 39.Use (a − b)² = a² − 2ab + b² to find 94².
40. 40.Find the value of x² + 2xy + y² when x = 3 and y = 1.

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