Problem 50 Apply the distributive property.... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 50

Apply the distributive property. $$-2\left(13-t^{2}\right)$$

Short Answer

Expert verified

The result is $-26 + 2t^2$.

Step by step solution

Understand the Distributive Property

The distributive property states that for any real numbers a, b, and c: $ a(b + c) = ab + ac $.In this case, we will apply the distributive property to the expression $ -2(13 - t^2) $.

Distribute -2 to Each Term Inside the Parentheses

Multiply $-2$ by each term inside the parentheses separately:$ -2 \times 13 $ and $ -2 \times -t^2 $.

Perform the Multiplications

Calculate the products obtained in Step 2:$ -2 \times 13 = -26 $$ -2 \times (-t^2) = 2t^2 $

Combine the Results

Combine the results from step 3 to form the final expression: $-26 + 2t^2$

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Key Concepts

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

Prealgebra

Prealgebra lays the foundation for all higher-level math. It's like learning the alphabet before writing sentences. In prealgebra, we focus on understanding basic mathematical operations and concepts, such as addition, subtraction, multiplication, and division.

We also explore properties and rules that help simplify expressions and solve equations. One such important property is the distributive property, which is fundamental as you progress to solving more complex algebraic expressions. By mastering prealgebra, you can build strong analytical and problem-solving skills that will be useful in both academics and everyday life.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables (like x or t), and mathematical operations (such as addition, subtraction, multiplication, and division). They can vary from simple to complex and are used to represent real-world situations in mathematical terms.

In our exercise, we have an algebraic expression: $-2(13 - t^2)$. Here, $-2$ is a constant multipler, while $13 - t^2$ is the expression inside the parentheses. To simplify this expression, we use the distributive property. Understanding how to combine and simplify terms in algebraic expressions is essential for solving equations and understanding functions.

Multiplication

Multiplication is one of the four elementary mathematical operations and is essentially repeated addition. For example, $3 \times 4$ means adding 3 four times: $3 + 3 + 3 + 3$.

When dealing with algebraic expressions, multiplication can involve numbers, variables, and even other expressions. Using the distributive property, you can multiply a term outside the parentheses by each term inside the parentheses.

In our exercise, we multiplied $-2$ by $13$ and $-2$ by $-t^2$ separately to simplify to $-26 + 2t^2$. This step-by-step multiplication helps us break down complex expressions into more manageable parts, making it easier to understand and solve.

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91影视

Apply the distributive property. $$-2\left(13-t^{2}\right)$$

Short Answer

Step by step solution

Understand the Distributive Property

Distribute -2 to Each Term Inside the Parentheses

Perform the Multiplications

Combine the Results

Key Concepts

Prealgebra

Algebraic Expressions

Multiplication

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