Final answer:
To rewrite the expression 24a⁵b - 6ab² by factoring out the common factor, we determine that the GCF is 6ab. Each term is divided by 6ab, resulting in the factorization of 6ab(4a⁴ - b).
Step-by-step explanation:
To rewrite the expression 24a⁵b - 6ab² by factoring out the common factor, we need to identify the greatest common factor (GCF) between the two terms. The first step in factoring expressions is to see what is common to each term. We can see that both terms have an 'a' and a 'b' variable and that the coefficients 24 and 6 share a common factor.
For the coefficients, the greatest common factor is 6. For the variables, we have a common 'a' (with the smallest exponent of 1) and a common 'b' (also with the smallest exponent of 1). So, the GCF is 6ab.
Now, we divide both terms by 6ab:
24a⁵b / 6ab = 4a⁴, and
6ab² / 6ab = b.
After dividing, we factor out the GCF from the original expression:
24a⁵b - 6ab² = 6ab(4a⁴ - b).
This process of factoring algebraic expressions simplifies the original problem and may be used to simplify further calculations or solve equations.