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When multiplying polynomials, we often use the distributive property. This property helps in breaking down expressions into smaller parts, making calculations simpler. The distributive property suggests that multiplying a single term by terms inside a parenthesis works like this: - Take the first term from the first polynomial and multiply it with every term of the second polynomial.- Do the same for each term of the first polynomial.
For example, in \((b+8)(6-2b)\), distribute each term in the first expression \(b+8\) over the terms in the second expression, resulting in:- \(b\times6\)- \(b\times(-2b)\)- \(8\times6\)- \(8\times(-2b)\)
By doing this, we ensure that every possible multiplication between the two sets of terms is covered. The result will be a new polynomial expression that can be simplified further.

Understanding like terms is crucial when combining terms in polynomial multiplication. Like terms are terms that have the same variable raised to the same power.- For instance, \(6b\) and \(-16b\) are like terms because they both have the variable \(b\) to the power of 1.
When combining like terms, you simply add or subtract their coefficients, which are the numerical parts in front of the variables. In our example, after distributing, we have:- \(6b\)- \(-16b\)
Since these are like terms, you combine them:\(6b - 16b = -10b\)
It's important to recognize like terms because they are the key to making an expression simpler and more manageable.

Once you've distributed the terms and identified the like terms, the next step is simplifying the expression. Simplifying means rewriting the expression in its simplest form by performing operations and combining like terms.
For the expression \(6b - 2b^2 + 48 - 16b\), this involves a few steps:- First, identify and reorder terms to easily see like terms.- Combine the like terms: - Combine \(6b\) and \(-16b\) to get \(-10b\).
After combining, the expression becomes:- \(-2b^2 - 10b + 48\)
The expression is now simpler, with all like terms combined, and it’s easier to evaluate for given values of \(b\) or to understand its behavior.