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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. 5.13 (page 492)

$Find the sum: (3 x^{2} - 4 x y + 5 y^{2}) + (2 x^{2} - x y)$

Short Answer

Expert verified

The sum of the given polynomials is $5 x^{2} 鈭� 5 x y + 5 y^{2}$

Step by step solution

01

Step 1. Given information

$\begin{array}{l} Thegivenpolynomialexpressionis \\ (3 x^{2} 鈭� 4 x y + 5 y^{2}) + (2 x^{2} 鈭� x y) \\ Wehavetofindthesum. \end{array}$

02

Step 2. Distribute and identify like terms

$\begin{array}{l} Wehave (3 x^{2} 鈭� 4 x y + 5 y^{2}) + (2 x^{2} 鈭� x y) \\ Distributeandidentifyliketermsandthenrearrangetheterms \\ 鈬� (3 x^{2} 鈭� 4 x y + 5 y^{2}) + (2 x^{2} 鈭� x y) = \underset{炉}{3 x^{2}} 鈭� \underset{炉}{\underset{炉}{4 x y}} + 5 y^{2} + \underset{炉}{2 x^{2}} 鈭� \underset{炉}{\underset{炉}{x y}} \\ = (3 + 2) x^{2} + (鈭� 4 鈭� 1) x y + 5 y^{2} \\ = 5 x^{2} 鈭� 5 x y + 5 y^{2} \end{array}$

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Write number (a) 1,290,000 (b) 0.00000103 in scientific notation

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