Problem 10 Simplify: $4 a b-15 a b$.... [FREE SOLUTION]

91影视

Elementary Algebra

David Arnold

$Math Studyset 91影视 Explanations$ Math

2020 Edition

Chapter 1: Problem 10

Simplify: $4 a b-15 a b$.

Short Answer

Expert verified

The simplified expression is $-11ab$.

Step by step solution

Identify Like Terms

In the expression $4ab - 15ab$, we first recognize that both terms $4ab$ and $-15ab$ have the same variable part, $ab$. This means they are like terms and can be combined by adding or subtracting their coefficients.

Subtract Coefficients

Since the terms are like terms, we subtract the coefficients of $ab$. The coefficients are 4 and -15. Calculate $4 - 15$, which equals -11. Therefore, $4ab - 15ab = (-11)ab$.

Write the Final Simplified Expression

Now that we've calculated the coefficients, we can write the final simplified expression as $-11ab$.

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Key Concepts

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

Like Terms

When working with algebraic expressions, identifying like terms is crucial for simplification. Like terms are terms that have the exact same variable components. In the expression $4ab - 15ab$, both terms have the variable part $ab$. This similarity means they can be combined through addition or subtraction.

To spot like terms, look for:

Matching variables and exponents
Similar terms can be grouped together to simplify expressions

Identifying like terms makes it easier to perform mathematical operations. It is the first step towards simplifying algebraic expressions effectively.

Combining Coefficients

Once like terms are identified, the next step is combining their coefficients. Coefficients are the numerical parts of the terms. In $4ab - 15ab$, the coefficients are 4 and -15.

The process involves simple arithmetic:

Add or subtract the coefficients
Keep the variable part the same (in this case, keep $ab$)

For our example, subtracting the coefficients 4 and -15 gives $4 - 15 = -11$.

Thus, $4ab - 15ab$ simplifies based on the combined coefficient, resulting in $-11ab$. This operation is straightforward but essential for simplifying expressions.

Algebraic Simplification

Algebraic simplification is the process of rewriting an expression in its simplest form. By doing so, the expression becomes easier to understand and solve. Let's break it down:

For $4ab - 15ab$:

Identify like terms (both involve $ab$)
Combine the coefficients (4 and -15) to get -11
Maintain the variable part, leading to $-11ab$

This results in a more concise expression. Simplification benefits:

Makes expressions easier to manipulate
Saves time in further operations
Reduces complexity for better clarity

Remember, the goal is to express your final answer in the most reduced and clear form possible.

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91影视

Simplify: \(4 a b-15 a b\).

Short Answer

Step by step solution

Identify Like Terms

Subtract Coefficients

Write the Final Simplified Expression

Key Concepts

Like Terms

Combining Coefficients

Algebraic Simplification

One App. One Place for Learning.

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