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Chapter 2: Problem 348

In the following exercises, simplify. $$ (4+3)(10-1) $$

Short Answer

Expert verified
63

Step by step solution

01

Identify and understand the expression

Given the expression \( (4+3)(10-1) \), recognize that this is a product of two binomials.
02

Simplify inside the parentheses

First, simplify each binomial inside the parentheses: \( 4 + 3 = 7 \) d \( 10 - 1 = 9 \)
03

Multiply the simplified values

Next, multiply the simplified results from each binomial: \( 7 \times 9 \)
04

Calculate the product

Finally, perform the multiplication: \( 7 \times 9 = 63 \)

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Key Concepts

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

Understanding Prealgebra
Prealgebra serves as the foundation for all advanced mathematics. Before diving into complicated topics, it's essential to understand basic operations, such as addition, subtraction, multiplication, and division. In our given problem, we use simple addition and subtraction before multiplying numbers.

When faced with any mathematical expression, the first step is always to simplify it as much as possible. This means resolving operations inside parentheses first. Mastering these fundamental skills in prealgebra can make complex problems easier and build confidence in solving them.
Working with Binomials
A binomial is an algebraic expression that consists of two terms, separated by either an addition or subtraction sign. In the example problem, we see two binomials: \( 4+3 \) and \( 10-1 \).

Understanding how to simplify these will help you break down the expression into smaller, manageable parts. When simplifying, always perform the operations inside the parentheses first. This approach clears out additional complexity and makes it easier to handle all components of the problem.

Ensuring you thoroughly grasp binomials will help you when you encounter more advanced algebraic expressions in the future.
Importance of Multiplication
Once you've simplified the binomials, the next step is multiplication. Multiplication is a fundamental mathematical operation that combines two numbers to find their product. In the problem, after simplifying the binomials to 7 and 9, you need to multiply these values: \( 7 \times 9 \).

Knowing your times tables or how to approach multiplication can speed up solving these problems. The product of 7 and 9 is 63, which is our final answer.

Practicing multiplication builds a strong mathematical foundation and helps solve more complex problems efficiently. So, always take your time to understand and practice this essential skill.

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Most popular questions from this chapter

In the following exercises, translate the given sentence into an algebraic equation and then solve it. The sum of r and 18 is 73.

In the following exercises, find the prime factorization of each number. $$ 572 $$

In the following exercises, solve each equation using the addition property of equality. $$ v-7=35 $$

In the following exercises, evaluate each expression. $$ h w \text { when } h=12, w=3 $$

In the following exercises, translate the given sentence into an algebraic equation. The sum of 7 and 9 is equal to 16.
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