Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 795 · 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 = 2 and ab = 24, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 20² − 12².
3. 3.Find the value of x² + 2xy + y² when x = 10 and y = 1.
4. 4.Use (a + b)² = a² + 2ab + b² to find 105².
5. 5.Use (a + b)(a − b) = a² − b² to find 21 × 19.
6. 6.Use a² − b² = (a + b)(a − b) to find 81² − 41².
7. 7.Find the value of x² − 2xy + y² when x = 9 and y = 1.
8. 8.Use a² − b² = (a + b)(a − b) to find 73² − 1².
9. 9.Use (a − b)² = a² − 2ab + b² to find 18².
10. 10.Use (a + b)² = a² + 2ab + b² to find 46².
11. 11.Use (a + b)(a − b) = a² − b² to find 97 × 83.
12. 12.Use (a + b)(a − b) = a² − b² to find 73 × 67.
13. 13.If a − b = 1 and ab = 6, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 79².
15. 15.Find the value of x² − 2xy + y² when x = 3 and y = 2.
16. 16.Find the value of x² − y² when x = 3 and y = 2.
17. 17.If a − b = 1 and ab = 12, what is a² + b²?
18. 18.If a − b = 4 and ab = 5, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 66².
20. 20.If a + b = 6 and ab = 8, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 74 × 66.
22. 22.Use (a + b)² = a² + 2ab + b² to find 102².
23. 23.Use a² − b² = (a + b)(a − b) to find 28² − 7².
24. 24.Use a² − b² = (a + b)(a − b) to find 61² − 48².
25. 25.Find the value of x² − 2xy + y² when x = 9 and y = 5.
26. 26.Use (a − b)² = a² − 2ab + b² to find 66².
27. 27.Use a² − b² = (a + b)(a − b) to find 88² − 72².
28. 28.If a + b = 3 and ab = 2, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 89 × 71.
30. 30.If a − b = 5 and ab = 6, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 23 × 17.
32. 32.If a + b = 9 and ab = 18, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 9 and y = 2.
34. 34.Use (a + b)² = a² + 2ab + b² to find 78².
35. 35.Use (a + b)(a − b) = a² − b² to find 69 × 51.
36. 36.If a − b = 7 and ab = 44, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 94² − 63².
38. 38.Use (a + b)(a − b) = a² − b² to find 37 × 23.
39. 39.If a + b = 13 and ab = 30, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 74² − 66².

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