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Q15.

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Found in: Page 33

### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

# Find the sum, difference or product.$\left(12x-7\right)-\left(5x-12\right)$

The difference $\left(12x-7\right)-\left(5x-12\right)=7x+5$

See the step by step solution

## Step 1. Apply the concept of addition and subtraction of polynomials.

We add and subtract polynomials using the properties of real numbers. The idea is to combine like terms (that is, terms with the same variables raised to the same powers) using the Distributive Property.

In subtracting polynomials, we have to remember that if a minus sign precedes an expression in parentheses, then the sign of every term within the parentheses is changed when we remove the parentheses.

## Step 2. Combine like terms.

Given $\left(12x-7\right)-\left(5x-12\right)$

Let us combine the terms with same variables raised to the same powers.

$\begin{array}{l}\left(12x-7\right)-\left(5x-12\right)=\left(12x-7\right)-5x+12\\ ⇒\left(12x-7\right)-\left(5x-12\right)=\left(12x-5x\right)+\left(-7+12\right)\end{array}$

## Step 3. Solve the expression.

From Step 2, we have:

$\begin{array}{l}\left(12x-7\right)-\left(5x-12\right)=\left(12x-5x\right)+\left(-7+12\right)\\ ⇒\left(12x-7\right)-\left(5x-12\right)=\left(12-5\right)x+\left(-7+12\right)\\ ⇒\left(12x-7\right)-\left(5x-12\right)=7x+5\end{array}$

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