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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 5.12 (page 492)

$Subtract (m^{2} - 7 m n - 3 n^{2}) from (m^{2} + n^{2})$

Short Answer

Expert verified

On subtracting $(m^{2} - 7 m n - 3 n^{2}) from (m^{2} + n^{2})$ we get $7 m n + 4 n^{2}$

Step by step solution

01

Step 1. Given information

We have to subtract $(m^{2} 鈭� 7 m n 鈭� 3 n^{2}) from (m^{2} + n^{2})$

This means we have to find

$(m^{2} + n^{2}) - (m^{2} 鈭� 7 m n 鈭� 3 n^{2})$

02

Step 2. Distribute and identify like terms

$\begin{array}{l} Wehave (m^{2} + n^{2}) 鈭� (m^{2} 鈭� 7 m n 鈭� 3 n^{2}) \\ Distributeandidentifyliketermsandthenrearrangetheterms \\ 鈬� (m^{2} + n^{2}) 鈭� (m^{2} 鈭� 7 m n 鈭� 3 n^{2}) = \underset{炉}{m^{2}} + \underset{炉}{\underset{炉}{n^{2}}} 鈭� \underset{炉}{m^{2}} + 7 m n + \underset{炉}{\underset{炉}{3 n^{2}}} \\ = (m^{2} 鈭� m^{2}) + 7 m n + (n^{2} + 3 n^{2}) \\ = 7 m n + 4 n^{2} \end{array}$

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