Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 79 · 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 a² − b² = (a + b)(a − b) to find 48² − 8².
2. 2.Use (a + b)² = a² + 2ab + b² to find 88².
3. 3.Find the value of x² − 2xy + y² when x = 3 and y = 1.
4. 4.Find the value of x² + 2xy + y² when x = 15 and y = 9.
5. 5.Find the value of x² − y² when x = 12 and y = 3.
6. 6.Use (a + b)(a − b) = a² − b² to find 23 × 17.
7. 7.Find the value of x² + 2xy + y² when x = 10 and y = 5.
8. 8.Use (a − b)² = a² − 2ab + b² to find 15².
9. 9.Use a² − b² = (a + b)(a − b) to find 75² − 15².
10. 10.Find the value of x² − 2xy + y² when x = 8 and y = 3.
11. 11.Find the value of x² + 2xy + y² when x = 12 and y = 7.
12. 12.Use (a + b)² = a² + 2ab + b² to find 89².
13. 13.Use (a + b)(a − b) = a² − b² to find 55 × 45.
14. 14.Find the value of x² − y² when x = 5 and y = 3.
15. 15.Use a² − b² = (a + b)(a − b) to find 64² − 54².
16. 16.Use (a + b)² = a² + 2ab + b² to find 72².
17. 17.If a + b = 9 and ab = 20, what is a² + b²?
18. 18.Find the value of x² + 2xy + y² when x = 13 and y = 1.
19. 19.Find the value of x² − 2xy + y² when x = 6 and y = 5.
20. 20.Use (a − b)² = a² − 2ab + b² to find 18².
21. 21.If a + b = 5 and ab = 6, what is a² + b²?
22. 22.Find the value of x² + 2xy + y² when x = 13 and y = 7.
23. 23.If a + b = 10 and ab = 21, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 31².
25. 25.Use (a + b)² = a² + 2ab + b² to find 68².
26. 26.Use (a + b)² = a² + 2ab + b² to find 62².
27. 27.If a + b = 13 and ab = 22, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 11².
29. 29.Use a² − b² = (a + b)(a − b) to find 23² − 5².
30. 30.If a − b = 8 and ab = 20, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 43 × 37.
32. 32.Use (a + b)(a − b) = a² − b² to find 79 × 61.
33. 33.Use (a + b)² = a² + 2ab + b² to find 59².
34. 34.Use (a + b)(a − b) = a² − b² to find 69 × 51.
35. 35.Use (a + b)(a − b) = a² − b² to find 64 × 56.
36. 36.If a + b = 11 and ab = 30, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 94 × 86.
38. 38.Use (a + b)(a − b) = a² − b² to find 32 × 28.
39. 39.Use (a − b)² = a² − 2ab + b² to find 65².
40. 40.Find the value of x² − y² when x = 8 and y = 7.

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