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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 6: Q. 65 (page 697)

In the following exercises, add or subtract the polynomials.
$(u^{2} - v^{2}) - (u^{2} - 4 u v - 3 v^{2})$

Short Answer

Expert verified

The simplified form is $2 v^{2} + 4 u v$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$(u^{2} - v^{2}) - (u^{2} - 4 u v - 3 v^{2})$

02

Step 2. Determine the value after simplification.

Simplify the given expression by combining the like terms.

$\begin{array}{rcl} (u^{2} - v^{2}) - (u^{2} - 4 u v - 3 v^{2}) & = & u^{2} - v^{2} - u^{2} + 4 u v + 3 v^{2} \\ = & (u^{2} - u^{2}) + (- v^{2} + 3 v^{2}) + 4 u v \\ = & (0) + 2 v^{2} + 4 u v \\ = & 2 v^{2} + 4 u v \end{array}$

03

Step 3. Conclusion.

The simplified form is $2 v^{2} + 4 u v$ .

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