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Chapter 0: Problem 11

Simplify each expression. $$ 2(m+p) $$

Short Answer

Expert verified
2m + 2p

Step by step solution

01

Distribute the Constant

To simplify the expression, distribute the constant 2 to both terms inside the parentheses.
02

Multiply Each Term

Multiply 2 by each term in the parentheses: 2 * m + 2 * p
03

Simplify Each Product

Calculate the results of the multiplication: 2m + 2p

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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 concept in algebra. It allows us to multiply a single term by each term inside a set of parentheses. For instance, with the expression \(2(m + p)\), we use the distributive property to expand it. This means you will multiply the 2 by both \(m\) and \(p\). This step results in \(2 * m + 2 * p\). Remember:

  • Distribute the constant to every term inside the parentheses.
  • This step ensures that each term is multiplied separately, which helps in simplifying the expression.
algebraic multiplication
Algebraic multiplication involves multiplying variables and constants. In our example, after applying the distributive property, we need to perform the actual multiplication:
  • Multiply 2 by \(m\): 2 \cdot m = 2m
  • Multiply 2 by \(p\): 2 \cdot p = 2p
This gives us the new expression. Each product keeps the variable with its coefficient. Always ensure:

  • Each multiplication is done carefully to avoid errors.
  • Variables remain attached to their coefficients after the multiplication.
simplification of expressions
Simplification of expressions is about combining and reducing expressions to their simplest form. After applying algebraic multiplication, we obtain 2m + 2p. Here, there's no further simplification since both terms are different:

  • Combine like terms (if any).
  • Ensure all arithmetic operations are completed.
The simplified form should have no parentheses, making the expression 2m + 2p our final answer.

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Most popular questions from this chapter

If \(a\) is a positive number, is \(-\sqrt{a}\) positive, negative, or not a real number?

Simplify each expression. $$ 6 \cdot 3-12 \div 4 $$

Write each fraction as a decimal. For repeating decimals, write the answer by first using bar notation and then rounding to the nearest thousandth. See Example 11. $$ \frac{5}{6} $$

The distributive property can be used to mentally perform calculations. $$\begin{array}{l}38 \cdot 17+38 \cdot 3 \\\=38(17+3) \\\=38(20) \\\=760\end{array} $$Use the distributive property to calculate each value mentally. $$ 8.75(15)-8.75(5) $$

Simplify each expression. $$ -8(\sqrt{64})-(-3)(-7) $$
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