SOLUTION: Find the LCM. y^3 + 8y^2 + 16y, y^2 - 8y

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the LCM. y^3 + 8y^2 + 16y, y^2 - 8y      Log On


   



Question 127153: Find the LCM.
y^3 + 8y^2 + 16y, y^2 - 8y

Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The factors of y%5E3+%2B+8y%5E2+%2B+16y are y, %28y%2B4%29, and %28y%2B4%29.

The factors of y%5E2+-+8y are y, and %28y-8%29,

Therefore the LCM needs:

1 factor of y,
2 factors of %28y%2B4%29, and
1 factor of %28y-8%29.

y%28y%2B4%29%28y%2B4%29%28y-8%29 is your LCM. I'll let you handle the expansion of the expression if you need it in that form.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E3+%2B+8y%5E2+%2B+16y …factor
y%28y%5E2+%2B+8y+%2B+16%29…..replace 8y with 4y+%2B+4y
y%28y%5E2+%2B+4y+%2B+4y+%2B+16%29…..group first 2 terms and second 2 terms together
y%28%28y%5E2+%2B+4y%29+%2B+%284y+%2B+16%29%29…..
y%28y%28y%2B+4%29+%2B+4%28y+%2B+4%29%29…..

y%28y%2B+4%29+%28y+%2B+4%29…..

y%5E2+-8y…factor
y%28y-8%29

so, the factors of y%5E3+%2B+8y%5E2+%2B+16yare: y +%28y+%2B+4%29 +%28y+%2B+4%29
and the factors of y%5E2+-8y are: y +%28y+-8%29
then
the Least Common Multiple (LCM) for y%5E3+%2B+8y%5E2+%2B+16y and y%5E2+-8y will be:
y+%28y+%2B+4%29+%28y+%2B+4%29+%28y+-8%29