91Ó°ÊÓ

When we talk about the common factor in mathematics, especially while factoring expressions, we refer to a term or number that is present in each part of an expression. Identifying these common factors is essential because it simplifies algebraic expressions.
In the given expression \(z(y-4)+3(y-4)\), we notice that \((y-4)\) is present in both terms. This means that \((y-4)\) is the common factor.
Understanding the implication of a common factor is crucial as it streamlines the process of factorization, allowing us to rewrite expressions in a more manageable, and often, solvable form. Whenever you see polynomials or expressions, always look for any term that repetitively appears across each of the components.

Algebraic expressions are combinations of numbers, variables, and arithmetic operations. They are foundational in algebra as they allow us to express mathematical ideas and relationships concisely.
In the expression \(z(y-4)+3(y-4)\), let's break it down:

• "\(z\)" is a variable that represents an unknown or changing number.
• "\(3\)" is a constant, a fixed number within the expression.
• "\((y-4)\)" is a binomial, an algebraic expression involving two terms.

Recognizing the structure of an algebraic expression helps us operate on it, whether simplifying, expanding, or factoring. Factoring often transforms complex expressions into simpler products of terms and is indispensable in solving equations.

Solving algebra problems step by step is like following a recipe. Each action builds on the previous one, leading to the correct "dish" or solution.
Let's walk through the factoring of the expression \(z(y-4)+3(y-4)\):

• First, we identify a common factor across all parts of our expression, which in this case is \((y-4)\).
• Once identified, we "factor out" this commonality from each term. It simplifies our expression and we obtain: \[(y-4)(z+3)\]

Taking it step by step is vital because it ensures every detail is accounted for, and mistakes are minimized. Remember, this approach has broad utility: not just in handling algebraic expressions, but across various problem-solving scenarios.