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