Problem 34 Subtract. $$ (-35 x+37)-(25 ... [FREE SOLUTION]

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Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 5: Problem 34

Subtract. $$ (-35 x+37)-(25 x-32) $$

Short Answer

Expert verified

The expression simplifies to $-60x + 69$.

Step by step solution

Distribution of Negative Sign

First, distribute the negative sign across the second set of parentheses. This changes the signs of the terms inside:\[ (-35x + 37) - (25x - 32) = -35x + 37 - 25x + 32 \]

Combine Like Terms

Now, combine the like terms. Combine the terms with $x$ and the constant terms separately:\[ -35x - 25x = -60x \] \[ 37 + 32 = 69 \]

Assemble Final Expression

Combine the results from Step 2 to form the final expression:\[ -60x + 69 \]

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Key Concepts

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

Subtracting Polynomials

Subtracting polynomials is a fundamental concept in algebra that involves finding the difference between two polynomial expressions. This means you need to change the subtraction problem into an addition problem by applying the negative sign to the entire polynomial being subtracted.

Think of subtracting polynomials as removing parts from one whole expression based on another. For example, with \[(-35x + 37) - (25x - 32)\], you are removing the second polynomial from the first. It's crucial to carefully manage the signs to avoid errors.

To streamline subtraction:

Apply the negative sign to each term in the second polynomial.
Rewrite the subtraction as addition of the opposite terms.

Following these steps ensures clarity and accuracy in your calculations.

Combining Like Terms

Once the negative sign has been distributed and the polynomials are set to be added together, the next critical step is to combine like terms. This involves grouping terms with the same variable and degree and performing simple arithmetic operations on their coefficients.

For the expression$-35x + 37 - 25x + 32$, like terms are those that include "$x$" and those that are constants:

Combine the terms with $x$ by adding their coefficients: $-35x - 25x = -60x$.
Combine constant terms: $37 + 32 = 69$.

Always remember:

Terms with the same variable are the only ones that can be combined.

Constant terms are considered like terms with each other and can be summed separately.

This method simplifies expressions and makes solving equations much clearer and manageable.

Distribution of Negative Sign

The distribution of a negative sign over an expression is essential when subtracting polynomials. This process involves reversing the signs of all terms in the expression that follows the negative sign. It transforms subtraction into addition of the opposite, which simplifies the management of expressions.

In the initial expression$-35x + 37 - (25x - 32)$, the negative sign in front of the parentheses requires distribution through these steps:

The negative sign is applied to $25x$, turning it into $-25x$.

The negative sign is applied to $-32$, changing it into $+32$.

Thus, the expression becomes $-35x + 37 - 25x + 32$.

Using this method prevents any sign errors when combining substances of equations or solving polynomials.

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91影视

Subtract. $$ (-35 x+37)-(25 x-32) $$

Short Answer

Step by step solution

Distribution of Negative Sign

Combine Like Terms

Assemble Final Expression

Key Concepts

Subtracting Polynomials

Combining Like Terms

Distribution of Negative Sign

One App. One Place for Learning.

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