Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 953 · 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 = 6 and ab = 8, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 44² − 29².
3. 3.Use a² − b² = (a + b)(a − b) to find 81² − 42².
4. 4.Find the value of x² + 2xy + y² when x = 15 and y = 7.
5. 5.Use (a + b)² = a² + 2ab + b² to find 26².
6. 6.Use a² − b² = (a + b)(a − b) to find 39² − 31².
7. 7.Use (a − b)² = a² − 2ab + b² to find 11².
8. 8.Use (a + b)² = a² + 2ab + b² to find 101².
9. 9.If a + b = 6 and ab = 5, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 61².
11. 11.Use (a − b)² = a² − 2ab + b² to find 29².
12. 12.Use (a + b)² = a² + 2ab + b² to find 13².
13. 13.Use (a + b)(a − b) = a² − b² to find 67 × 53.
14. 14.Find the value of x² − 2xy + y² when x = 13 and y = 6.
15. 15.Use (a + b)(a − b) = a² − b² to find 34 × 26.
16. 16.If a + b = 11 and ab = 28, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 77².
18. 18.Use (a + b)(a − b) = a² − b² to find 85 × 75.
19. 19.Use (a − b)² = a² − 2ab + b² to find 98².
20. 20.If a + b = 5 and ab = 4, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 17².
22. 22.Use (a − b)² = a² − 2ab + b² to find 79².
23. 23.Find the value of x² − y² when x = 6 and y = 5.
24. 24.Use (a + b)² = a² + 2ab + b² to find 42².
25. 25.Use (a + b)(a − b) = a² − b² to find 93 × 87.
26. 26.Use (a − b)² = a² − 2ab + b² to find 28².
27. 27.Find the value of x² − 2xy + y² when x = 4 and y = 3.
28. 28.If a + b = 10 and ab = 9, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 72 × 68.
30. 30.Use (a + b)² = a² + 2ab + b² to find 49².
31. 31.Use (a − b)² = a² − 2ab + b² to find 36².
32. 32.Use (a + b)(a − b) = a² − b² to find 62 × 58.
33. 33.If a + b = 19 and ab = 84, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 59² − 10².
35. 35.If a + b = 8 and ab = 7, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 12².
37. 37.Use (a + b)(a − b) = a² − b² to find 101 × 99.
38. 38.Find the value of x² + 2xy + y² when x = 10 and y = 6.
39. 39.Use (a + b)² = a² + 2ab + b² to find 54².
40. 40.Use (a + b)² = a² + 2ab + b² to find 32².

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