Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 81 · 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 = 10 and y = 5.
2. 2.If a − b = 2 and ab = 3, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 66².
4. 4.Use (a + b)² = a² + 2ab + b² to find 67².
5. 5.If a + b = 17 and ab = 70, what is a² + b²?
6. 6.Find the value of x² − y² when x = 6 and y = 4.
7. 7.Use (a + b)(a − b) = a² − b² to find 21 × 19.
8. 8.Use (a − b)² = a² − 2ab + b² to find 21².
9. 9.Use a² − b² = (a + b)(a − b) to find 72² − 47².
10. 10.If a + b = 10 and ab = 24, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 78².
12. 12.Use (a + b)(a − b) = a² − b² to find 94 × 86.
13. 13.Use (a + b)² = a² + 2ab + b² to find 81².
14. 14.Use (a − b)² = a² − 2ab + b² to find 37².
15. 15.Use (a − b)² = a² − 2ab + b² to find 69².
16. 16.Use (a − b)² = a² − 2ab + b² to find 38².
17. 17.Use (a + b)² = a² + 2ab + b² to find 82².
18. 18.Use a² − b² = (a + b)(a − b) to find 43² − 8².
19. 19.If a − b = 2 and ab = 35, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 45 × 35.
21. 21.If a − b = 8 and ab = 20, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 36 × 24.
23. 23.If a + b = 5 and ab = 6, what is a² + b²?
24. 24.If a − b = 1 and ab = 132, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 43².
26. 26.Use (a + b)² = a² + 2ab + b² to find 48².
27. 27.Use (a + b)² = a² + 2ab + b² to find 31².
28. 28.Use a² − b² = (a + b)(a − b) to find 79² − 26².
29. 29.Find the value of x² − y² when x = 9 and y = 2.
30. 30.Use a² − b² = (a + b)(a − b) to find 69² − 19².
31. 31.Use (a + b)² = a² + 2ab + b² to find 39².
32. 32.If a − b = 1 and ab = 2, what is a² + b²?
33. 33.If a + b = 15 and ab = 56, what is a² + b²?
34. 34.Find the value of x² − 2xy + y² when x = 4 and y = 1.
35. 35.Use (a − b)² = a² − 2ab + b² to find 98².
36. 36.Use (a + b)² = a² + 2ab + b² to find 98².
37. 37.Use (a − b)² = a² − 2ab + b² to find 77².
38. 38.Use (a − b)² = a² − 2ab + b² to find 97².
39. 39.Use a² − b² = (a + b)(a − b) to find 64² − 29².
40. 40.Use (a + b)² = a² + 2ab + b² to find 11².

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