Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 955 · 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.Find the value of x² + 2xy + y² when x = 11 and y = 2.
2. 2.If a + b = 16 and ab = 55, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 32 × 28.
4. 4.Use (a + b)(a − b) = a² − b² to find 44 × 36.
5. 5.Use (a − b)² = a² − 2ab + b² to find 11².
6. 6.If a − b = 10 and ab = 24, what is a² + b²?
7. 7.If a + b = 14 and ab = 48, what is a² + b²?
8. 8.If a − b = 6 and ab = 7, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 38 × 22.
10. 10.Use (a + b)² = a² + 2ab + b² to find 103².
11. 11.Use (a + b)² = a² + 2ab + b² to find 41².
12. 12.Use (a + b)(a − b) = a² − b² to find 81 × 79.
13. 13.If a + b = 7 and ab = 12, what is a² + b²?
14. 14.If a − b = 1 and ab = 2, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 68².
16. 16.Use (a − b)² = a² − 2ab + b² to find 39².
17. 17.Use (a − b)² = a² − 2ab + b² to find 49².
18. 18.Find the value of x² + 2xy + y² when x = 4 and y = 1.
19. 19.Find the value of x² − y² when x = 13 and y = 4.
20. 20.Use (a − b)² = a² − 2ab + b² to find 75².
21. 21.Find the value of x² − y² when x = 8 and y = 4.
22. 22.If a + b = 3 and ab = 2, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 47².
24. 24.If a − b = 4 and ab = 5, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 56² − 48².
26. 26.Find the value of x² − y² when x = 3 and y = 1.
27. 27.Find the value of x² + 2xy + y² when x = 7 and y = 4.
28. 28.Use (a + b)(a − b) = a² − b² to find 66 × 54.
29. 29.If a − b = 1 and ab = 72, what is a² + b²?
30. 30.If a + b = 14 and ab = 24, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 109 × 91.
32. 32.Use a² − b² = (a + b)(a − b) to find 66² − 61².
33. 33.Use (a + b)² = a² + 2ab + b² to find 29².
34. 34.Use (a + b)² = a² + 2ab + b² to find 95².
35. 35.Use (a + b)² = a² + 2ab + b² to find 32².
36. 36.Use (a − b)² = a² − 2ab + b² to find 44².
37. 37.Use (a + b)(a − b) = a² − b² to find 55 × 45.
38. 38.Use (a − b)² = a² − 2ab + b² to find 24².
39. 39.Use (a + b)(a − b) = a² − b² to find 102 × 98.
40. 40.If a + b = 8 and ab = 12, what is a² + b²?

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