Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 954 · 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 73² − 32².
2. 2.If a + b = 7 and ab = 12, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 92².
4. 4.Use (a − b)² = a² − 2ab + b² to find 17².
5. 5.Find the value of x² − y² when x = 14 and y = 13.
6. 6.Use (a + b)(a − b) = a² − b² to find 61 × 59.
7. 7.Use a² − b² = (a + b)(a − b) to find 24² − 17².
8. 8.Use (a − b)² = a² − 2ab + b² to find 48².
9. 9.Use (a + b)² = a² + 2ab + b² to find 92².
10. 10.Use (a + b)² = a² + 2ab + b² to find 17².
11. 11.Use (a − b)² = a² − 2ab + b² to find 34².
12. 12.Use (a − b)² = a² − 2ab + b² to find 94².
13. 13.Use (a + b)(a − b) = a² − b² to find 27 × 13.
14. 14.Use (a − b)² = a² − 2ab + b² to find 64².
15. 15.Use a² − b² = (a + b)(a − b) to find 43² − 26².
16. 16.Use (a + b)² = a² + 2ab + b² to find 93².
17. 17.Use (a + b)(a − b) = a² − b² to find 32 × 28.
18. 18.Use (a − b)² = a² − 2ab + b² to find 84².
19. 19.If a + b = 3 and ab = 2, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 76².
21. 21.Find the value of x² − y² when x = 3 and y = 2.
22. 22.Use a² − b² = (a + b)(a − b) to find 30² − 5².
23. 23.Find the value of x² + 2xy + y² when x = 10 and y = 9.
24. 24.Use (a − b)² = a² − 2ab + b² to find 37².
25. 25.Use (a + b)² = a² + 2ab + b² to find 61².
26. 26.Use a² − b² = (a + b)(a − b) to find 44² − 41².
27. 27.Use a² − b² = (a + b)(a − b) to find 48² − 18².
28. 28.Use (a + b)(a − b) = a² − b² to find 79 × 61.
29. 29.Use (a + b)² = a² + 2ab + b² to find 108².
30. 30.Use (a + b)² = a² + 2ab + b² to find 37².
31. 31.If a + b = 7 and ab = 10, what is a² + b²?
32. 32.If a + b = 14 and ab = 40, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 8 and y = 3.
34. 34.Use (a − b)² = a² − 2ab + b² to find 39².
35. 35.Use a² − b² = (a + b)(a − b) to find 51² − 28².
36. 36.Use a² − b² = (a + b)(a − b) to find 88² − 1².
37. 37.Use (a + b)² = a² + 2ab + b² to find 47².
38. 38.Use a² − b² = (a + b)(a − b) to find 38² − 18².
39. 39.If a + b = 15 and ab = 56, what is a² + b²?
40. 40.If a − b = 1 and ab = 2, what is a² + b²?

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