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Understanding common factors is essential when factoring algebraic expressions. A common factor in algebra is a number or term that divides all terms in an expression without a remainder. For example, in the expression \(2a + 2b\), the common factor is \(2\) because both \(2a\) and \(2b\) can be divided by \(2\). Identifying these common factors simplifies expressions and prepares them for further factoring.
Take the expression from the exercise: \(xy + xz + wy + wz\). Notice here, each term is composed of variables and coefficients, but there isn’t a single common factor for all four terms.
Instead, you can look at grouping pairs of terms to exploit common factors within subsets of the entire expression.

Grouping terms is a strategy used for simplifying an algebraic expression by organizing it into smaller, more manageable parts. This technique is extremely useful when direct factoring isn’t straightforward.
In the provided example, the expression \(xy + xz + wy + wz\) can be divided into pairs such that we can identify common factors more easily. For instance, we can pair \(xy\) with \(xz\), and \(wy\) with \(wz\).
When grouping, the idea is to rearrange or pair the terms so that each pair has a common factor, making it easier to factor them individually:

• Group 1: \(xy + xz\)
• Group 2: \(wy + wz\)

This method of grouping terms enables us to factor out common factors from each pair, which aids in further simplification.

Once terms have been grouped, you can use the common factors within each group to simplify the expression further. This process is called factoring by grouping.
For the expression \(xy + xz + wy + wz\), after grouping the terms, you identified the following pairs: \(xy + xz\) and \(wy + wz\).
You can factor out common factors from each group individually:

• \(xy + xz = x(y + z)\)
• \(wy + wz = w(y + z)\)

Now you have: \(x(y + z) + w(y + z)\).
The final step is to factor out the common binomial group, \((y + z)\), from the expression: \((y + z)(x + w)\).
This technique turns complex algebraic expressions into simpler, more understandable forms, proving the power of factoring by grouping.