Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 210 · 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 56 × 44.
2. 2.Find the value of x² + 2xy + y² when x = 13 and y = 2.
3. 3.Use (a + b)(a − b) = a² − b² to find 52 × 48.
4. 4.If a − b = 1 and ab = 2, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 49 × 31.
6. 6.Use a² − b² = (a + b)(a − b) to find 43² − 8².
7. 7.Use (a + b)(a − b) = a² − b² to find 53 × 47.
8. 8.Use (a − b)² = a² − 2ab + b² to find 18².
9. 9.Use (a + b)² = a² + 2ab + b² to find 15².
10. 10.Use (a + b)² = a² + 2ab + b² to find 67².
11. 11.Use a² − b² = (a + b)(a − b) to find 98² − 18².
12. 12.Use a² − b² = (a + b)(a − b) to find 47² − 32².
13. 13.Find the value of x² − 2xy + y² when x = 3 and y = 1.
14. 14.If a − b = 2 and ab = 35, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 89².
16. 16.Use a² − b² = (a + b)(a − b) to find 84² − 45².
17. 17.Use (a + b)(a − b) = a² − b² to find 25 × 15.
18. 18.Use a² − b² = (a + b)(a − b) to find 81² − 17².
19. 19.Use (a + b)² = a² + 2ab + b² to find 52².
20. 20.Use (a + b)² = a² + 2ab + b² to find 26².
21. 21.Use (a − b)² = a² − 2ab + b² to find 38².
22. 22.If a − b = 2 and ab = 24, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 77² − 39².
24. 24.Use (a + b)² = a² + 2ab + b² to find 35².
25. 25.Use (a + b)(a − b) = a² − b² to find 41 × 39.
26. 26.If a + b = 8 and ab = 7, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 93².
28. 28.Use (a − b)² = a² − 2ab + b² to find 72².
29. 29.Use (a + b)(a − b) = a² − b² to find 28 × 12.
30. 30.If a + b = 12 and ab = 20, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 14².
32. 32.If a − b = 1 and ab = 6, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 52² − 45².
34. 34.Use (a + b)² = a² + 2ab + b² to find 85².
35. 35.Use (a + b)² = a² + 2ab + b² to find 66².
36. 36.Find the value of x² − 2xy + y² when x = 8 and y = 7.
37. 37.Find the value of x² − 2xy + y² when x = 11 and y = 10.
38. 38.Find the value of x² + 2xy + y² when x = 5 and y = 3.
39. 39.Find the value of x² − y² when x = 3 and y = 1.
40. 40.Use (a − b)² = a² − 2ab + b² to find 17².

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