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An algebraic expression is a mathematical phrase that can contain numbers, variables, and operational symbols. In the given exercise, we have an expression: \(10(p+7)\). Here, the number 10 is called a coefficient, and it is multiplied by the expression inside the parentheses \((p+7)\). The expression inside the parentheses consists of a variable 'p' and a constant '7'.

Understanding algebraic expressions is crucial because they are the building blocks of algebra. They allow us to show relationships between different quantities and can easily be manipulated using various algebraic techniques, such as the distributive property, to solve equations and simplify expressions.

• Variables represent unknown values and can be any letter or symbol.
• Coefficients are numbers that multiply a variable in an algebraic expression.
• Constants are fixed numbers contained within the expression.

Learning how to identify each part of an algebraic expression helps with more complex problem-solving scenarios.

Simplifying an expression involves performing all possible operations and combining like terms. This process makes an expression easier to work with and understand.

In our exercise, the expression \(10(p+7)\) was simplified through the distributive property. Initially, we expanded the expression by multiplying each term inside the parentheses by 10. This resulted in the expression: \(10p + 70\). Since there are no like terms to combine, the expression is already simplified. Simplification can involve:

• Combining like terms: These are terms that have the same variable raised to the same power.
• Using arithmetic operations: This includes addition, subtraction, multiplication, and division.
• Applying the distributive property: Used to expand expressions neatly.

Simplifying helps in solving equations more efficiently and reduces potential errors during calculations.

Mathematical operations are the procedures we use to combine numbers and variables to form expressions. In this exercise, we primarily used multiplication and addition.

The distributive property requires us to multiply a number by each term inside parentheses and then sum the results. For our expression \(10(p+7)\), we performed the following:

1. Multiply the coefficient 10 by each of the terms inside the parentheses: \(10 \times p\) and \(10 \times 7\).
2. Add the products: \(10p + 70\).

These operations allowed us to simplify the expression without changing its value. The core mathematical operations include:

• Addition and subtraction: Used to combine numbers and like terms.
• Multiplication and division: Used to distribute numbers across terms or break down complex terms, respectively.
• Exponentiation and roots: Involve powers and extracting roots, for more advanced expressions.

Mastering these operations is essential for solving algebra problems and working with numbers efficiently.