SOLUTION: Factor each expression. 1. 216x^3 – 1 2. 8x^3 + 125 3. x^4 – 5x^2 + 4 Please any help???

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor each expression. 1. 216x^3 – 1 2. 8x^3 + 125 3. x^4 – 5x^2 + 4 Please any help???      Log On


   

Question 546994: Factor each expression.
1. 216x^3 – 1
2. 8x^3 + 125
3. x^4 – 5x^2 + 4
Please any help???
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
1. 216x%5E3-1 This is a difference of two cubes which can be factored thus:
A%5E3-B%5E3+=+%28A-B%29%28A%5E2%2BAB%2BB%5E2%29
216x%5E3-1+=+%286x%29%5E3-%281%29%5E3=highlight%28%286x-1%29%2836x%5E2%2B6x%2B1%29%29
2. 8x%5E3%2B125 This is a sum of two cubes which can be factored thus:
A%5E3%2BB%5E3+=+%28A%2BB%29%28A%5E2-AB%2BB%5E2%29
8x%5E3%2B125+=+%282x%29%5E3%2B%285%29%5E3=highlight%28%282x%2B5%29%284x%5E2-10x%2B25%29%29
3. x%5E4-5x%5E2%2B4 Temporarily change the varible: x%5E2+=+y
y%5E2-5y%2B4+=+%28y-1%29%28y-4%29 Substitute y+=+x%5E2
%28x%5E2-1%29%28x%5E2-4%29+=+highlight%28%28x%2B1%29%28x-1%29%28x%5E2%2B4%29%29