-8a⁵b²+12a³b⁴=

To factor the expression \(-8a^5b^2 + 12a^3b^4\), we can start by finding the greatest common factor (GCF) of the two terms.

1. Identify the GCF of the coefficients:

   • The coefficients are -8 and 12. The GCF of 8 and 12 is 4.

2. Identify the GCF of the variables:

   • For \(a\): The minimum power is \(a^3\) (since \(a^5\) and \(a^3\) are in the expression).
   • For \(b\): The minimum power is \(b^2\) (since \(b^2\) and \(b^4\) are in the expression).

So the GCF of the entire expression is \(4a^3b^2\).

Now, we can factor the GCF out of each term:

\[ -8a^5b^2 + 12a^3b^4 = 4a^3b^2(-2a^2 + 3b^2) \]

Thus, the factored form of the expression is:

\[ 4a^3b^2(-2a^2 + 3b^2) \]