SOLUTION: Factor the expression, if possible. x^4 - 1296 Please enter "prime ", if the expression cannot be factored.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the expression, if possible. x^4 - 1296 Please enter "prime ", if the expression cannot be factored.       Log On


   

Question 103787This question is from textbook beginning and intermediate algebra
: Factor the expression, if possible.
x^4 - 1296

Please enter "prime ", if the expression cannot be factored.



This question is from textbook beginning and intermediate algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To factor this, simply use the difference of squares

a%5E2-b%5E2=%28a%2Bb%29%28a-b%29


So let a=x^2 (it is the square root of x%5E4) and b=36 (it is the square root of 1296) to get


%28x%5E2%29%5E2-%2836%29%5E2=%28x%5E2%2B36%29%28x%5E2-36%29


Now factor x%5E2-36 to %28x%2B6%29%28x-6%29. Again use the difference of squares to factor


So x%5E4+-+1296 factors to %28x%5E2%2B36%29%28x%2B6%29%28x-6%29