Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 784 · 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 = 18 and ab = 80, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 52 × 48.
3. 3.Use (a + b)(a − b) = a² − b² to find 99 × 81.
4. 4.Use (a − b)² = a² − 2ab + b² to find 74².
5. 5.Use (a + b)² = a² + 2ab + b² to find 32².
6. 6.Use (a + b)(a − b) = a² − b² to find 93 × 87.
7. 7.If a − b = 1 and ab = 6, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 57².
9. 9.Use (a + b)² = a² + 2ab + b² to find 84².
10. 10.Use (a + b)² = a² + 2ab + b² to find 37².
11. 11.If a + b = 5 and ab = 6, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 22² − 20².
13. 13.If a + b = 19 and ab = 84, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 75² − 9².
15. 15.Use a² − b² = (a + b)(a − b) to find 61² − 10².
16. 16.Use (a + b)² = a² + 2ab + b² to find 49².
17. 17.Use (a + b)(a − b) = a² − b² to find 67 × 53.
18. 18.Find the value of x² − y² when x = 13 and y = 2.
19. 19.Find the value of x² − y² when x = 6 and y = 1.
20. 20.Use (a + b)(a − b) = a² − b² to find 28 × 12.
21. 21.Find the value of x² + 2xy + y² when x = 5 and y = 4.
22. 22.If a − b = 9 and ab = 36, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 12².
24. 24.Use a² − b² = (a + b)(a − b) to find 76² − 33².
25. 25.Use (a − b)² = a² − 2ab + b² to find 36².
26. 26.Use (a − b)² = a² − 2ab + b² to find 16².
27. 27.If a − b = 1 and ab = 2, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 28².
29. 29.Use (a + b)(a − b) = a² − b² to find 42 × 38.
30. 30.Find the value of x² − y² when x = 3 and y = 1.
31. 31.If a + b = 5 and ab = 4, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 33 × 27.
33. 33.Use a² − b² = (a + b)(a − b) to find 52² − 50².
34. 34.Use (a + b)(a − b) = a² − b² to find 88 × 72.
35. 35.Use (a + b)(a − b) = a² − b² to find 48 × 32.
36. 36.Find the value of x² − 2xy + y² when x = 15 and y = 11.
37. 37.Find the value of x² − y² when x = 4 and y = 2.
38. 38.Find the value of x² + 2xy + y² when x = 14 and y = 4.
39. 39.Use (a + b)² = a² + 2ab + b² to find 44².
40. 40.Find the value of x² − 2xy + y² when x = 12 and y = 3.

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