Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 310 · 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 = 4 and y = 2.
2. 2.Find the value of x² + 2xy + y² when x = 14 and y = 3.
3. 3.Use a² − b² = (a + b)(a − b) to find 63² − 38².
4. 4.Use a² − b² = (a + b)(a − b) to find 51² − 48².
5. 5.Use (a − b)² = a² − 2ab + b² to find 28².
6. 6.Use (a − b)² = a² − 2ab + b² to find 43².
7. 7.Use (a + b)² = a² + 2ab + b² to find 27².
8. 8.Find the value of x² − y² when x = 6 and y = 2.
9. 9.Use a² − b² = (a + b)(a − b) to find 79² − 41².
10. 10.Use (a + b)² = a² + 2ab + b² to find 65².
11. 11.Use (a − b)² = a² − 2ab + b² to find 77².
12. 12.Use a² − b² = (a + b)(a − b) to find 66² − 56².
13. 13.Use (a + b)² = a² + 2ab + b² to find 103².
14. 14.Use (a + b)² = a² + 2ab + b² to find 47².
15. 15.If a + b = 16 and ab = 55, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 65² − 15².
17. 17.Find the value of x² − y² when x = 8 and y = 5.
18. 18.Find the value of x² − 2xy + y² when x = 14 and y = 7.
19. 19.If a − b = 1 and ab = 90, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 32².
21. 21.Use (a − b)² = a² − 2ab + b² to find 36².
22. 22.Use (a + b)² = a² + 2ab + b² to find 49².
23. 23.Use (a + b)² = a² + 2ab + b² to find 14².
24. 24.Use (a + b)(a − b) = a² − b² to find 56 × 44.
25. 25.Use (a + b)(a − b) = a² − b² to find 65 × 55.
26. 26.Find the value of x² + 2xy + y² when x = 6 and y = 2.
27. 27.Use (a + b)² = a² + 2ab + b² to find 79².
28. 28.Use (a − b)² = a² − 2ab + b² to find 73².
29. 29.Use (a + b)(a − b) = a² − b² to find 36 × 24.
30. 30.Use (a + b)(a − b) = a² − b² to find 96 × 84.
31. 31.Use (a + b)(a − b) = a² − b² to find 106 × 94.
32. 32.Use (a + b)(a − b) = a² − b² to find 94 × 86.
33. 33.Use (a + b)² = a² + 2ab + b² to find 37².
34. 34.If a + b = 19 and ab = 90, what is a² + b²?
35. 35.If a + b = 9 and ab = 14, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 29 × 11.
37. 37.If a + b = 12 and ab = 27, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 89².
39. 39.Use (a − b)² = a² − 2ab + b² to find 46².
40. 40.Find the value of x² − y² when x = 10 and y = 4.

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