Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 885 · 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 53² − 51².
2. 2.Use (a + b)(a − b) = a² − b² to find 76 × 64.
3. 3.Use (a − b)² = a² − 2ab + b² to find 91².
4. 4.Use a² − b² = (a + b)(a − b) to find 21² − 14².
5. 5.Use (a + b)(a − b) = a² − b² to find 72 × 68.
6. 6.If a + b = 15 and ab = 36, what is a² + b²?
7. 7.Find the value of x² − y² when x = 10 and y = 8.
8. 8.If a + b = 11 and ab = 30, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 43².
10. 10.Use (a − b)² = a² − 2ab + b² to find 67².
11. 11.If a + b = 13 and ab = 42, what is a² + b²?
12. 12.Find the value of x² + 2xy + y² when x = 15 and y = 3.
13. 13.Use (a + b)(a − b) = a² − b² to find 52 × 48.
14. 14.Find the value of x² − 2xy + y² when x = 7 and y = 5.
15. 15.Use (a + b)(a − b) = a² − b² to find 43 × 37.
16. 16.Use (a − b)² = a² − 2ab + b² to find 66².
17. 17.Use (a + b)² = a² + 2ab + b² to find 82².
18. 18.Find the value of x² − 2xy + y² when x = 11 and y = 5.
19. 19.Use a² − b² = (a + b)(a − b) to find 99² − 61².
20. 20.If a − b = 6 and ab = 7, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 24² − 1².
22. 22.If a − b = 1 and ab = 2, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 48 × 32.
24. 24.Find the value of x² − y² when x = 4 and y = 1.
25. 25.Use (a + b)² = a² + 2ab + b² to find 32².
26. 26.Use (a − b)² = a² − 2ab + b² to find 68².
27. 27.If a − b = 1 and ab = 12, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 61².
29. 29.Use a² − b² = (a + b)(a − b) to find 70² − 65².
30. 30.Find the value of x² + 2xy + y² when x = 14 and y = 2.
31. 31.Use (a + b)² = a² + 2ab + b² to find 63².
32. 32.Use (a + b)² = a² + 2ab + b² to find 52².
33. 33.Use (a − b)² = a² − 2ab + b² to find 79².
34. 34.Find the value of x² + 2xy + y² when x = 9 and y = 6.
35. 35.Use (a + b)² = a² + 2ab + b² to find 72².
36. 36.Find the value of x² + 2xy + y² when x = 4 and y = 2.
37. 37.Use a² − b² = (a + b)(a − b) to find 23² − 9².
38. 38.Use (a − b)² = a² − 2ab + b² to find 18².
39. 39.Use (a − b)² = a² − 2ab + b² to find 11².
40. 40.Use (a + b)(a − b) = a² − b² to find 54 × 46.

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