Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 316 · 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 = 5 and ab = 66, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 67².
3. 3.Find the value of x² − y² when x = 4 and y = 3.
4. 4.Use (a − b)² = a² − 2ab + b² to find 19².
5. 5.Use (a + b)² = a² + 2ab + b² to find 102².
6. 6.Use (a + b)² = a² + 2ab + b² to find 85².
7. 7.Use (a − b)² = a² − 2ab + b² to find 25².
8. 8.Use (a − b)² = a² − 2ab + b² to find 68².
9. 9.If a + b = 12 and ab = 20, what is a² + b²?
10. 10.Find the value of x² − 2xy + y² when x = 10 and y = 6.
11. 11.If a − b = 5 and ab = 50, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 84².
13. 13.Use (a + b)² = a² + 2ab + b² to find 32².
14. 14.Use (a + b)(a − b) = a² − b² to find 25 × 15.
15. 15.Use (a + b)(a − b) = a² − b² to find 49 × 31.
16. 16.Find the value of x² + 2xy + y² when x = 8 and y = 1.
17. 17.Use (a + b)(a − b) = a² − b² to find 43 × 37.
18. 18.Use (a − b)² = a² − 2ab + b² to find 89².
19. 19.Find the value of x² − 2xy + y² when x = 14 and y = 2.
20. 20.Use (a − b)² = a² − 2ab + b² to find 59².
21. 21.Find the value of x² + 2xy + y² when x = 4 and y = 2.
22. 22.Use (a − b)² = a² − 2ab + b² to find 61².
23. 23.Use (a + b)² = a² + 2ab + b² to find 14².
24. 24.Use (a + b)² = a² + 2ab + b² to find 93².
25. 25.Use (a + b)(a − b) = a² − b² to find 87 × 73.
26. 26.Use a² − b² = (a + b)(a − b) to find 73² − 57².
27. 27.Find the value of x² + 2xy + y² when x = 4 and y = 1.
28. 28.Use (a + b)² = a² + 2ab + b² to find 11².
29. 29.Use a² − b² = (a + b)(a − b) to find 44² − 14².
30. 30.Use a² − b² = (a + b)(a − b) to find 40² − 39².
31. 31.Use a² − b² = (a + b)(a − b) to find 84² − 49².
32. 32.Find the value of x² − y² when x = 6 and y = 4.
33. 33.Use a² − b² = (a + b)(a − b) to find 42² − 31².
34. 34.Use a² − b² = (a + b)(a − b) to find 52² − 26².
35. 35.Use (a + b)² = a² + 2ab + b² to find 103².
36. 36.Use (a + b)(a − b) = a² − b² to find 23 × 17.
37. 37.Use a² − b² = (a + b)(a − b) to find 83² − 63².
38. 38.Use (a + b)(a − b) = a² − b² to find 62 × 58.
39. 39.If a − b = 3 and ab = 108, what is a² + b²?
40. 40.If a + b = 6 and ab = 8, what is a² + b²?

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