SOLUTION: I cant understand this formula for the sum of differences. my example is 8y^3-1

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Question 710732: I cant understand this formula for the sum of differences. my example is 8y^3-1
Found 2 solutions by fcabanski, lwsshak3:
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
There's not much to understand. The formula is like a recipe...plug in the numbers and variables.


a%5E3-b%5E3=%28a-b%29%2A%28a%5E2%2Bab%2Bb%5E2%29


Recognize that the initial expression is the difference of two cubes. 8y%5E3=%282y%29%5E3%29 so a=2y. 1=1%5E3 so b=1.


The factored form is %282y-1%29%2A%28%282y%29%5E2%2B%282y%2A1%29%2B1%5E2%29=%282y-1%29%2A%284y%5E2%2B2y%2B1%29

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)


Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
I cant understand this formula for the sum of differences. my example is 8y^3-1
**
Formula for the difference of two cubes: x%5E3-y%5E3=%28x-y%29%28x%5E2%2Bxy%2By%5E2%29
For your example, it becomes clearer when you write the expression as a difference of two cubes.
8y%5E3-1=%282y%29%5E3-1%5E3=%282y-1%29%284y%5E2%2B2y%2B1%29
remember:
1%5E3=1