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When working with algebraic expressions, identifying common factors is an important step in simplifying and factoring. A common factor is a number or variable that divides two or more terms without leaving a remainder. Let's take the expression given in the problem: \[7p + 14q\]. Both terms in this expression (7p and 14q) share the number 7 as a common factor. To identify this, check each term:
- The first term, 7p, includes the factor 7.
- The second term, 14q, can be factored as 7 × 2q.
Recognizing such common factors is the first step toward factoring an entire algebraic expression efficiently.

Once a common factor is identified, the next step is to factor it out from the algebraic expression. Factoring out means rewriting the expression such that the common factor is placed outside a set of parentheses, and what's left inside represents the remaining parts of each term after dividing by the common factor.
In the exercise, we identified 7 as the common factor for both terms in the expression 7p + 14q. To factor out 7, divide each term by 7:
- For the first term: 7p ÷ 7 = p
- For the second term: 14q ÷ 7 = 2q
Therefore, factoring out the 7, the expression becomes 7(p + 2q). This step simplifies the original expression and makes it easier to work with.

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation signs. In this exercise, the given algebraic expression is \[7p + 14q\]. Algebraic expressions can be simplified and factored to make them more manageable.
Factoring is particularly useful because it helps in solving equations and simplifying expressions. In our case, the expression \[7p + 14q\] was factored by identifying and factoring out the common factor of 7, resulting in 7(p + 2q). This new expression is much simpler and easier to handle.
Simplifying algebraic expressions by factoring is a fundamental skill in algebra, aiding in various operations and solving more complex problems.