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Chapter 1: Problem 739

Simplify. $$ 7(4 a) $$

Short Answer

Expert verified
28a

Step by step solution

01

Distribute the 7

Multiply the 7 by each term inside the parentheses. Since there is only one term inside the parentheses, just multiply 7 by 4a.
02

Perform the multiplication

Calculate 7 multiplied by 4a. This involves multiplying the numeric coefficients (7 and 4) and keeping the variable (a).
03

Combine the coefficients

Multiply 7 and 4 to get 28, and keep the variable a. Therefore, 7(4a) simplifies to 28a.

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Key Concepts

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

distributive property
The distributive property is a fundamental rule in algebra that allows us to simplify expressions by distributing a multiplication over addition or subtraction inside parentheses. In simpler terms, if you have an expression in the form of **a(b + c)**, applying the distributive property lets you rewrite it as **ab + ac**. This property ensures you can break down problems into smaller, more manageable parts. In our specific problem, we only had one term inside the parentheses, so we just multiplied it directly: **7(4a)**.
multiplication of coefficients
When dealing with algebraic expressions involving multiplication, you often come across coefficients, which are the numerical parts of terms. Multiplying coefficients is a crucial step in simplifying these expressions. For instance, in the given exercise, we multiplied the coefficients 7 and 4. Here鈥檚 the detailed process:

  • Identify the coefficients in the terms. In **7(4a)**, the coefficients are 7 and 4.
  • Multiply the coefficients together. So, we calculate **7 * 4** to get 28.

Once multiplied, keep the variable part (in this case, 'a') as it is. Thus, **7(4a)** becomes **28a**.
algebraic simplification
Algebraic simplification involves combining like terms and performing operations to rewrite expressions in their simplest form. Here鈥檚 the simplified breakdown of our problem:

  • Start with: **7(4a)**
  • Apply the distributive property: Multiply 7 by each term inside the parentheses. Since there's only one term, we directly multiply 7 by **4a**.
  • Perform multiplication: Calculate **7 * 4**. This gives us 28.
  • Combine the coefficients: Rewrite the expression with the multiplied coefficients and the variable as **28a**.

Through these steps, we took the initial expression and simplified it, highlighting each part's role in reaching the final, simplest form: **28a**.

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