Question

How do you factor completely `8 a^2 x^5 y^4 + 10 a^3 x^3 y^4 + 14 a^2 + x^3 y^7`?

Answer 1

Assuming one typo in the question...

`8a^2x^5y^4+10a^3x^3y^4+14a^2x^3y^7 = 2a^2x^3y^4(4x^2+5a+y^3)`

Explanation:

This question has no really useful answer in the form given in that it has no simpler factors.

I suspect that there is a typo in the question, whereby the last two terms should be a single term `14a^2x^3y^7`, though even that does not look very reasonable...

Consider:

`8a^2x^5y^4+10a^3x^3y^4+14a^2x^3y^7`

All of the terms are divisible by `2`, `a^2`, `x^3` and `y^4`.

Hence we find:

`8a^2x^5y^4+10a^3x^3y^4+14a^2x^3y^7 = 2a^2x^3y^4(4x^2+5a+y^3)`

This does not factor any further.