Question

How do you factor `18u ^ { 5} x ^ { 8} + 12u x ^ { 2} y ^ { 4}`?

Answer 1

Factor this by finding the greatest common factor for each variable and constant in each term.

Explanation:

`18u^5x^8 + 12ux^2y^4` can be rewritten as:

`(3 xx 3 xx 2 xx u xx u^4 xx x^2 xx x^6) + (3 xx 2 xx 2 xx u xx x^2 xx y^4)`

The common factors are in red and can be factored out of the expression as follows:

`(color(red)(3) xx 3 xx color(red)(2) xx color(red)(u) xx u^4 xx color(red)(x^2) xx x^6) + (color(red)(3) xx color(red)(2) xx 2 xx color(red)(u) xx color(red)(x^2) xx y^4) =`

`(color(red)(3 xx 2 xx u xx x^2))((3 xx u^4 xx x^6) + (2 xx y^4)) =`

`6ux^2(3u^4x^6 + 2y^4)`