Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 646 · 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)(a − b) = a² − b² to find 93 × 87.
2. 2.Use a² − b² = (a + b)(a − b) to find 33² − 31².
3. 3.Use (a + b)² = a² + 2ab + b² to find 104².
4. 4.Find the value of x² − y² when x = 8 and y = 2.
5. 5.Use a² − b² = (a + b)(a − b) to find 91² − 17².
6. 6.Use (a + b)(a − b) = a² − b² to find 102 × 98.
7. 7.Use (a + b)² = a² + 2ab + b² to find 22².
8. 8.Use (a − b)² = a² − 2ab + b² to find 44².
9. 9.Use (a + b)² = a² + 2ab + b² to find 35².
10. 10.Use (a + b)² = a² + 2ab + b² to find 73².
11. 11.Use a² − b² = (a + b)(a − b) to find 97² − 74².
12. 12.Find the value of x² − y² when x = 15 and y = 5.
13. 13.Use a² − b² = (a + b)(a − b) to find 47² − 8².
14. 14.Use a² − b² = (a + b)(a − b) to find 51² − 22².
15. 15.Use a² − b² = (a + b)(a − b) to find 79² − 12².
16. 16.Use (a + b)² = a² + 2ab + b² to find 38².
17. 17.Use (a + b)² = a² + 2ab + b² to find 69².
18. 18.Use (a − b)² = a² − 2ab + b² to find 37².
19. 19.Use a² − b² = (a + b)(a − b) to find 65² − 64².
20. 20.Use a² − b² = (a + b)(a − b) to find 24² − 3².
21. 21.Use (a + b)² = a² + 2ab + b² to find 89².
22. 22.If a − b = 8 and ab = 9, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 24 × 16.
24. 24.Find the value of x² − y² when x = 15 and y = 7.
25. 25.Use a² − b² = (a + b)(a − b) to find 89² − 4².
26. 26.Use (a + b)(a − b) = a² − b² to find 97 × 83.
27. 27.Use a² − b² = (a + b)(a − b) to find 85² − 20².
28. 28.If a + b = 5 and ab = 6, what is a² + b²?
29. 29.If a − b = 1 and ab = 12, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 64² − 20².
31. 31.If a − b = 7 and ab = 18, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 56² − 48².
33. 33.Use (a + b)(a − b) = a² − b² to find 26 × 14.
34. 34.Use (a + b)(a − b) = a² − b² to find 25 × 15.
35. 35.Use (a + b)(a − b) = a² − b² to find 37 × 23.
36. 36.Use (a − b)² = a² − 2ab + b² to find 45².
37. 37.If a − b = 5 and ab = 24, what is a² + b²?
38. 38.If a − b = 2 and ab = 3, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 72².
40. 40.Use a² − b² = (a + b)(a − b) to find 43² − 21².

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