How do you factor 12x7y9+6x4y7−10x3y5?

You need to pull the highest common value out of each variable and constant in the terms:
For the constants 12, 6 and 10 the highest common value is 2
For x the highest common value is ${\displaystyle x^3}$
For y the highest common value is ${\displaystyle y^5}$
So, we can rewrite this problem, using the rules for exponents as:
${\displaystyle 2x^3{y}^5(6x^{7-3}{y}^{9-5}+3x^{4-3}{y}^{7-5}-5x^{3-3}{y}^{5-5})\Rightarrow }$
${\displaystyle 2x^3{y}^5(6x^4{y}^4+3x^1{y}^2-5x^0{y}^0)\Rightarrow }$
${\displaystyle 2x^3{y}^5(6x^4{y}^4+3x{y}^2-5\cdot 1\cdot 1)\Rightarrow }$
${\displaystyle 2x^3{y}^5(6x^4{y}^4+3x{y}^2-5)}$