Question

How do you factor out the GCF of `8x ^ { 3} y ^ { 2} - 4x ^ { 2} y ^ { 3} + 14x y ^ { 4}`?

Answer 1

`8x ^ { 3} y ^ { 2} - 4x ^ { 2} y ^ { 3} + 14x y ^ { 4}`
`= 2xy^2(4x^2 -2xy + 7y^2)`
`" "uarrcolor(white)(xxxxxx)uarr`
`=HCF (' "left-overs' from each term")`

Explanation:

`8x ^ { 3} y ^ { 2} - 4x ^ { 2} y ^ { 3} + 14x y ^ { 4}`

First identify what factors are common in each term. This includes the indices.

By inspection, we see `2 and x and y^2" "larr`this is the `HCF`

Now DIVIDE each term by the HCF and write the quotients,
(the left-overs), in a bracket:

`8x ^ { 3} y ^ { 2} - 4x ^ { 2} y ^ { 3} + 14x y ^ { 4}`

`= 2xy^2(4x^2 -2xy + 7y^2)`