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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. 34 (page 498)

In the following exercises, add the polynomials.
$(4 y^{2} + 10 y + 3) + (8 y^{2} - 6 y + 5)$

Short Answer

Expert verified

The sum of the polynomials is $12 y^{2} + 4 y + 8$

Step by step solution

01

Step 1. Given information

$\begin{array}{l} Thegivenexpressionis \\ (4 y^{2} + 10 y + 3) + (8 y^{2} 鈭� 6 y + 5) \\ Wehavetoaddthepolynomials. \end{array}$

02

Step 2. Add the polynomials

$\begin{array}{l} 鈬� (4 y^{2} + 10 y + 3) + (8 y^{2} 鈭� 6 y + 5) \\ = 4 y^{2} + 10 y + 3 + 8 y^{2} 鈭� 6 y + 5 [Rewritewithouttheparenthese] \\ = 4 y^{2} + 8 y^{2} + 10 y 鈭� 6 y + 3 + 5 [Combinetheliketerms] \\ = (4 + 8) y^{2} + (10 鈭� 6) y + 8 \\ = 12 y^{2} + 4 y + 8 \end{array}$

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Most popular questions from this chapter

Solve the square using the binomial squares pattern.

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

Solve the square using the binomial squares pattern.

${(\frac{1}{5} x - \frac{1}{7} y)}^{2}$

Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial

$(a) 64 k^{3} - 8 (b) 9 m^{3} + 4 m^{2} - 2 (c) \frac{5}{6} (d) 8 a^{4} - 7 a^{3} b - 6 a^{2} b^{2} - 4 a b^{3} + 7 b^{4} (e) - p^{4} q^{3}$

In the following exercises, multiply the binomials using a) the Distributive Property; b) the FOIL method; c) the Vertical Method

$(7 q + 4) (3 q - 8)$

Multiply each pair of conjugates using the product of the conjugates pattern.

$(15 m^{2} - 8 n^{4}) (15 m^{2} + 8 n^{4})$

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