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In algebra, we often deal with algebraic expressions. These are mathematical phrases that can include numbers, variables, and operation signs. For example, in the expression \(5x^4\), 5 is the coefficient, and \(x^4\) is the variable term.
Algebraic expressions can be simple or complex, but they play a fundamental role in many mathematical problems. Understanding how to manipulate and simplify these expressions is crucial for solving equations and real-world problems.

The distributive property is a key algebraic property used to simplify expressions and solve equations. This property states that \(a(b + c) = ab + ac\). In other words, you distribute the multiplication across each term inside the parentheses. In the original problem, we use the distributive property to multiply the constant 6 by the coefficient 5 and the variable \(x^4\).
Here's how the distributive property works in this case:* Identify the expression: \((5x^4) \times 6\)* Distribute the 6 to each term inside: \(6 \times 5x^4\)* Perform the multiplication: \(6 \times 5 = 30\)* Combine the result: \(30x^4\).
As you can see, the distributive property helps you break down the multiplication into manageable steps.

Coefficients are the numerical parts of terms in algebraic expressions. They indicate how many times a variable is being multiplied. In the expression \(5x^4\), the number 5 is the coefficient. In algebra, terms can have coefficients of any real number.* A coefficient can be positive or negative.* It can be an integer, a fraction, or a decimal.
Identifying the coefficients in an expression helps you understand its structure and perform calculations more effectively. For example, in our problem, the coefficient 5 is multiplied by 6 to yield 30, which is then combined with the variable term \(x^4\), resulting in \(30x^4\). By understanding coefficients, you can simplify expressions and solve equations more easily.