Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 257 · 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)² = a² + 2ab + b² to find 15².
2. 2.If a − b = 3 and ab = 4, what is a² + b²?
3. 3.Find the value of x² + 2xy + y² when x = 5 and y = 3.
4. 4.If a − b = 5 and ab = 36, what is a² + b²?
5. 5.Find the value of x² − y² when x = 6 and y = 5.
6. 6.If a + b = 3 and ab = 2, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 62².
8. 8.Use (a − b)² = a² − 2ab + b² to find 78².
9. 9.Use (a + b)(a − b) = a² − b² to find 43 × 37.
10. 10.Use (a + b)(a − b) = a² − b² to find 52 × 48.
11. 11.Find the value of x² − 2xy + y² when x = 3 and y = 2.
12. 12.Find the value of x² − y² when x = 6 and y = 2.
13. 13.Use a² − b² = (a + b)(a − b) to find 37² − 30².
14. 14.If a + b = 5 and ab = 4, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 12².
16. 16.Use (a + b)(a − b) = a² − b² to find 79 × 61.
17. 17.Use (a + b)² = a² + 2ab + b² to find 42².
18. 18.Use (a − b)² = a² − 2ab + b² to find 69².
19. 19.If a + b = 4 and ab = 3, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 67².
21. 21.If a − b = 2 and ab = 63, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 79² − 39².
23. 23.If a − b = 7 and ab = 8, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 98².
25. 25.Use (a + b)(a − b) = a² − b² to find 106 × 94.
26. 26.If a + b = 5 and ab = 6, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 49² − 36².
28. 28.Use (a + b)² = a² + 2ab + b² to find 63².
29. 29.If a − b = 1 and ab = 2, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 64² − 58².
31. 31.Use (a − b)² = a² − 2ab + b² to find 37².
32. 32.Use (a + b)² = a² + 2ab + b² to find 29².
33. 33.If a + b = 12 and ab = 27, what is a² + b²?
34. 34.Find the value of x² + 2xy + y² when x = 15 and y = 2.
35. 35.Use (a − b)² = a² − 2ab + b² to find 48².
36. 36.If a + b = 11 and ab = 30, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 74 × 66.
38. 38.Use (a − b)² = a² − 2ab + b² to find 56².
39. 39.Use a² − b² = (a + b)(a − b) to find 94² − 44².
40. 40.Use a² − b² = (a + b)(a − b) to find 29² − 24².

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