Factor out the greatest common factor from the expression
9a2b3 – 12a2b4 – 24a3b
9a^2b^3 - 12a^2b^4 - 24a^3b.
3a^2b(3b^2 - 4b^3 - 8a).
To factor out the greatest common factor from the expression 9a^2b^3 – 12a^2b^4 – 24a^3b, we need to identify the common factors that all the terms share, and then divide each term by that factor.
Step 1: Identify the common factors. In this expression, the coefficients 9, 12, and 24 share a common factor of 3. The variables a^2, a^2, and a^3 share a common factor of a^2. And the variables b^3, b^4, and b share a common factor of b.
Step 2: Divide each term by the common factors.
9a^2b^3 ÷ 3a^2b = 3ab^2
-12a^2b^4 ÷ 3a^2b = -4b^3
-24a^3b ÷ 3a^2b = -8ab^2
Step 3: Write the expression with the factored out greatest common factor.
The factored form of the expression 9a^2b^3 – 12a^2b^4 – 24a^3b is:
3ab^2 - 4b^3 - 8ab^2