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Q15.

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Precalculus Mathematics for Calculus

Found in: Page 33

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

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

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 $(12 x - 7) - (5 x - 12)$

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

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

Step 3. Solve the expression.

From Step 2, we have:

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

Most popular questions for Math Textbooks

Mary’s backyard vegetable garden measures 20 ft by 30 ft, so its area is $20 \times 30 = 600 {ft}^{2}$ . She decides to make it longer, as shown in the figure so that the area increases to $A =20(30+ x)$ . Which property of real numbers tells us that the new area can also be written $A = 600 + 20 x$ ?

Simplify the fractional expression.

$\frac{{(7 - 3 x)}^{\frac{1}{2}} + \frac{3}{2} x {(7 - 3 x)}^{- \frac{1}{2}}}{7 - 3 x}$

Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms and state its degree.

Polynomial	Type	Term	Degree
$5 x^{3} + 6$

Question: 1. Give an example of each of the following:

A natural number
An integer that is not a natural number
A rational number that is not an integer
An irrational number

Simplify the fractional expression.

$\frac{2 x {(x + 6)}^{4} - x^{2} (4) {(x + 6)}^{3}}{{(x + 6)}^{8}}$

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