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Chapter 5: Problem 102

Simplify. (Assume variables are nonzero.) $$ 5 x 0 y 2 $$

Short Answer

Expert verified
The simplified expression is 0.

Step by step solution

01

Identify Multiplication by Zero

The expression given is \(5 \cdot x \cdot 0 \cdot y \cdot 2\). Notice that one of the factors in this multiplication is 0. Any number multiplied by zero is zero.
02

Simplify using Zero Property of Multiplication

According to the zero property of multiplication, if any term in a product is zero, the entire product is zero. Therefore, without needing to do further multiplication, the expression simplifies directly to 0.

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Key Concepts

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

Understanding Multiplication
Multiplication is a basic mathematical operation. It involves combining equal groups of objects. Think of it as adding the same number over and over.

For instance, multiplying 3 by 4 means you have four groups of 3 added together:
  • 3 + 3 + 3 + 3 = 12
In an algebraic context, we often multiply variables and numbers together. Like with the expression given, this might involve terms like \(5 \cdot x \cdot 0 \cdot y \cdot 2\).

One crucial thing to remember is the zero property of multiplication. If any number in a sequence being multiplied is zero, the whole product becomes zero. This helps simplify expressions quickly and effectively.
Simplification Made Simple
Simplification involves breaking down complex expressions into their simplest form. It makes calculations easier to understand and solve.

In multiplication, especially involving zero, simplification is straightforward. When you see a zero, you know the entire expression can be simplified immediately to zero. This is due to the zero property of multiplication.

For example, in the expression \(5 \cdot x \cdot 0 \cdot y \cdot 2\), you don't need to bother multiplying any other numbers. As soon as you spot the zero, you can say, "The answer is zero!" This process saves time and avoids confusion.
Navigating Algebraic Expressions
Algebraic expressions can seem tricky at first. They are combinations of numbers, variables, and operations like addition and multiplication.

In our example, we have variables \(x\) and \(y\) alongside numbers. It's important to remember these variables typically represent unknown values or quantities. When simplifying such expressions, focus on any special properties of operations involved.
  • Pay attention to the multiplication rules, especially the zero property.
  • Use these properties to reduce expressions quickly.
Knowing these basics allows you to tackle algebraic problems with more confidence and efficiency.

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