91Ó°ÊÓ

Simplifying expressions is a key skill in algebra. It involves reducing an algebraic expression to its simplest form.
The main goal is to make the expression easier to work with, often by eliminating parentheses and combining like terms.
When simplifying, always follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
For example, in the expression -7(4p + 1), you start by focusing on the parentheses.
Always look for opportunities to apply properties like the Distributive Property to break down complex expressions into simpler parts. This process makes solving equations and understanding relationships between variables much more manageable.

Algebraic multiplication involves multiplying coefficients and variables.
In our exercise, we see -7(4p + 1). Here, -7 is multiplied by both 4p and 1.
This showcases the Distributive Property: \(a(b+c)=ab+ac\).
First, multiply -7 by 4p: \(-7 * 4p\). This gives us \(-28p\).
Next, multiply -7 by 1: \(-7 * 1\), which results in \-7\.
The Distributive Property is especially useful when dealing with parentheses in algebraic expressions, as it allows you to systematically break down and simplify the equation step-by-step.
Remember, each term within the parentheses must be multiplied by the term outside before proceeding to any additional simplification steps.

After using algebraic multiplication, the next step is combining like terms.
Like terms are terms that have the same variables raised to the same power.
For example, in the expression -28p - 7, there aren't any like terms to combine since -28p has a variable part and -7 is a constant.
However, if you had an expression like \(-28p - 7 + 5p\), you would combine -28p and 5p to get \(-23p\).
Always identify and group like terms first before performing any addition or subtraction.
This process simplifies expressions and makes solving equations more direct and less error-prone.