Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 961 · 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)(a − b) = a² − b² to find 21 × 19.
2. 2.If a − b = 2 and ab = 3, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 93².
4. 4.If a + b = 3 and ab = 2, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 62².
6. 6.Use (a + b)(a − b) = a² − b² to find 34 × 26.
7. 7.Use (a + b)² = a² + 2ab + b² to find 41².
8. 8.Use (a − b)² = a² − 2ab + b² to find 14².
9. 9.Use (a + b)(a − b) = a² − b² to find 24 × 16.
10. 10.Use (a − b)² = a² − 2ab + b² to find 74².
11. 11.Use (a + b)(a − b) = a² − b² to find 23 × 17.
12. 12.Use (a − b)² = a² − 2ab + b² to find 68².
13. 13.Use a² − b² = (a + b)(a − b) to find 66² − 14².
14. 14.Use a² − b² = (a + b)(a − b) to find 71² − 1².
15. 15.Use (a + b)(a − b) = a² − b² to find 67 × 53.
16. 16.Find the value of x² − y² when x = 11 and y = 2.
17. 17.Find the value of x² − 2xy + y² when x = 12 and y = 9.
18. 18.Find the value of x² − y² when x = 12 and y = 6.
19. 19.Use (a + b)² = a² + 2ab + b² to find 48².
20. 20.If a + b = 12 and ab = 11, what is a² + b²?
21. 21.Find the value of x² + 2xy + y² when x = 12 and y = 7.
22. 22.Use (a + b)² = a² + 2ab + b² to find 102².
23. 23.Use (a − b)² = a² − 2ab + b² to find 95².
24. 24.Use (a + b)(a − b) = a² − b² to find 84 × 76.
25. 25.Use a² − b² = (a + b)(a − b) to find 53² − 43².
26. 26.Use (a + b)(a − b) = a² − b² to find 35 × 25.
27. 27.Find the value of x² + 2xy + y² when x = 5 and y = 2.
28. 28.Use (a + b)² = a² + 2ab + b² to find 104².
29. 29.Use (a + b)² = a² + 2ab + b² to find 31².
30. 30.Find the value of x² + 2xy + y² when x = 6 and y = 5.
31. 31.Use a² − b² = (a + b)(a − b) to find 23² − 1².
32. 32.Use (a − b)² = a² − 2ab + b² to find 61².
33. 33.Use a² − b² = (a + b)(a − b) to find 22² − 1².
34. 34.Find the value of x² − 2xy + y² when x = 9 and y = 5.
35. 35.Use (a + b)² = a² + 2ab + b² to find 12².
36. 36.Find the value of x² + 2xy + y² when x = 8 and y = 6.
37. 37.Use (a + b)(a − b) = a² − b² to find 106 × 94.
38. 38.Use (a − b)² = a² − 2ab + b² to find 88².
39. 39.Use (a + b)² = a² + 2ab + b² to find 107².
40. 40.Use a² − b² = (a + b)(a − b) to find 82² − 28².

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