Problem 795 Simplify using the distributive ... [FREE SOLUTION]

Chapter 1: Problem 795

Simplify using the distributive property. $$ -7(4 p+1) $$

Short Answer

Expert verified

-28p - 7

Step by step solution

Apply the Distributive Property

The distributive property states that for any numbers a, b, and c: ewline $a(b + c) = ab + ac$. ewline Apply this property to ewline -7(4p + 1) by distributing -7 to both terms inside the parentheses.

Multiply -7 with the First Term

Multiply -7 by 4p: ewline $-7 \times 4p = -28p$.

Multiply -7 with the Second Term

Multiply -7 by 1: ewline $-7 \times 1 = -7$.

Combine the Results

Combine the results from the previous steps to get the simplified expression: ewline $-28p - 7$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

simplifying expressions

Simplifying expressions is a foundational skill in algebra. It involves reducing an expression to its simplest form by performing operations and combining like terms.
When you simplify, you might add or subtract terms, multiply factors, or use algebraic properties like the distributive property.
Simplified expressions make it easier to solve equations and understand relationships between variables.
Always look for operations you can perform and terms you can combine to make the expression as straightforward as possible.

algebraic operations

Algebraic operations include addition, subtraction, multiplication, and division applied to variables and constants.
Unlike arithmetic, where you only work with numbers, algebra involves symbols (like p or x) that represent numbers.
Here are a few essential points to remember:

Addition/Subtraction: Combine like terms (terms with the same variable raised to the same power).
Multiplication: Use the distributive property to multiply a single term by multiple terms inside parentheses.
Division: Spread the divisor across each term within the numerator if possible.

Understanding how to correctly apply these operations ensures that you can handle any algebraic expression.

multiplication in algebra

Multiplication in algebra often involves the distributive property, especially when dealing with expressions in parentheses.
The distributive property tells us that multiplying a single term by a sum of terms (inside parentheses) requires us to multiply the single term by each term in the sum.
For example, in the problem $ -7(4p + 1) $, we distribute -7 to each term inside the parentheses: $ -7 \times 4p = -28p $ and $ -7 \times 1 = -7 $.
This property helps in breaking down complex expressions, making them simpler and easier to work with.
Remember, always apply multiplication carefully, ensuring each term is accounted for.

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91影视

Simplify using the distributive property. $$ -7(4 p+1) $$

Short Answer

Step by step solution

Apply the Distributive Property

Multiply -7 with the First Term

Multiply -7 with the Second Term

Combine the Results

Key Concepts

simplifying expressions

algebraic operations

multiplication in algebra

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