Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 273 · 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)² = a² − 2ab + b² to find 46².
2. 2.Use (a + b)(a − b) = a² − b² to find 27 × 13.
3. 3.If a + b = 18 and ab = 72, what is a² + b²?
4. 4.If a − b = 6 and ab = 55, what is a² + b²?
5. 5.Find the value of x² + 2xy + y² when x = 3 and y = 1.
6. 6.Use (a + b)² = a² + 2ab + b² to find 68².
7. 7.If a + b = 3 and ab = 2, what is a² + b²?
8. 8.Find the value of x² − 2xy + y² when x = 14 and y = 2.
9. 9.Find the value of x² − y² when x = 5 and y = 4.
10. 10.Use a² − b² = (a + b)(a − b) to find 55² − 36².
11. 11.Use (a + b)² = a² + 2ab + b² to find 48².
12. 12.If a + b = 10 and ab = 9, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 68 × 52.
14. 14.Use (a + b)² = a² + 2ab + b² to find 43².
15. 15.Use (a + b)² = a² + 2ab + b² to find 28².
16. 16.Use (a + b)(a − b) = a² − b² to find 103 × 97.
17. 17.Use (a − b)² = a² − 2ab + b² to find 86².
18. 18.Use (a − b)² = a² − 2ab + b² to find 25².
19. 19.Find the value of x² − 2xy + y² when x = 3 and y = 2.
20. 20.Use a² − b² = (a + b)(a − b) to find 88² − 78².
21. 21.If a − b = 11 and ab = 12, what is a² + b²?
22. 22.If a − b = 4 and ab = 5, what is a² + b²?
23. 23.Find the value of x² + 2xy + y² when x = 15 and y = 6.
24. 24.Use a² − b² = (a + b)(a − b) to find 64² − 39².
25. 25.Use (a − b)² = a² − 2ab + b² to find 39².
26. 26.Use (a + b)(a − b) = a² − b² to find 33 × 27.
27. 27.Use a² − b² = (a + b)(a − b) to find 21² − 10².
28. 28.Use (a + b)² = a² + 2ab + b² to find 38².
29. 29.If a + b = 10 and ab = 16, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 98 × 82.
31. 31.Use (a + b)² = a² + 2ab + b² to find 94².
32. 32.Use a² − b² = (a + b)(a − b) to find 82² − 68².
33. 33.Use (a − b)² = a² − 2ab + b² to find 48².
34. 34.Use (a + b)(a − b) = a² − b² to find 42 × 38.
35. 35.Use (a + b)(a − b) = a² − b² to find 23 × 17.
36. 36.Use (a + b)(a − b) = a² − b² to find 38 × 22.
37. 37.Find the value of x² + 2xy + y² when x = 7 and y = 4.
38. 38.Use (a + b)² = a² + 2ab + b² to find 103².
39. 39.Find the value of x² − y² when x = 14 and y = 3.
40. 40.Use a² − b² = (a + b)(a − b) to find 79² − 71².

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