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Polynomial multiplication is a process where we multiply two or more polynomials together to get a single polynomial.
It involves distributing each term in one polynomial by every term in the other.
Here's how to think about it:

• Each term in the first polynomial must be multiplied by each term in the second polynomial.
• If there are multiple terms, you need to perform several multiplications and then sum these up.

In our exercise, the original task was \(-3b(2b^2 - b)\). We begin by distributing, or multiplying each term individually.
This turns our task into calculating the product of \(-3b \) with \(2b^2 \) and also with \(-b\).
Once both multiplications are complete, you combine these results to find the expanded polynomial.

Simplifying expressions involves reducing them to their most compact and manageable form.
The process seeks to make expressions easier to work with and understand.
To simplify, we often:

• Combine like terms.
• Use mathematical operations to make the expression as simple as possible.

In our task, after distributing \(-3b\) and obtaining the terms \(-6b^3\) and \(+3b^2\), we stop at this point because there are no like terms to combine further.
This means the expression \(-6b^3 + 3b^2\) is as simplified as possible for the given exercise.
Unlike numbers, polynomials are simplified by adjusting terms until no further like terms or simplifications can be made.

The distributive property is a crucial algebraic concept that lets us multiply a single term by each term within a set of parentheses.
This property states that \(a(b + c) = ab + ac\), where \(a\), \(b\), and \(c\) are any numbers or expressions.
Essentially, each term inside the parentheses should be treated separately in multiplication, ensuring no terms are left out.In the exercise, we applied the distributive property by multiplying \(-3b\) with each term inside the parentheses: \(2b^2\) and \(-b\).
By correctly applying this property, an expression that looks complex at first glance becomes straightforward.
Using the distributive property, therefore, forms the backbone of simplifying algebraic expressions, as it allows us to systematically break down and solve expressions.