33) $$ 15 a b-2 b^{2}-6 a+5 b^{3} $$

Question

UpStudy AI · Accepted Answer

We start with the expression

$$
15ab - 2b^2 - 6a + 5b^3.
$$

**Step 1. Rearrange the Terms**

Group the terms to help with the factorization:

$$
(15ab - 6a) + (-2b^2 + 5b^3).
$$

**Step 2. Factor by Grouping**

Factor out common factors from each group.

For the first group $$15ab - 6a$$, factor out $$3a$$:

$$
15ab - 6a = 3a(5b - 2).
$$

For the second group $$-2b^2 + 5b^3$$, factor out $$b^2$$:

$$
-2b^2 + 5b^3 = b^2(-2 + 5b) = b^2(5b - 2).
$$

**Step 3. Factor Out the Common Binomial**

Now, the expression becomes:

$$
3a(5b - 2) + b^2(5b - 2).
$$

Since both terms share the common factor $$(5b - 2)$$, we factor it out:

$$
(5b - 2)(3a + b^2).
$$

Thus, the fully factored form of the expression is

$$
(5b - 2)(3a + b^2).
$$
The expression $$15ab - 2b^2 - 6a + 5b^3$$ can be factored as $$(5b - 2)(3a + b^2)$$.

33) \( 15 a b-2 b^{2}-6 a+5 b^{3} \)