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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.440R (page 561)

Multiply the binomials by using
(a) The Distributive property (b) the FOIL method (c) the Vertical method.
$(3 x + 1) (2 x - 7)$ .

Short Answer

Expert verified

(a) Using the distributive property $(3 x + 1) (2 x - 7) = 6 x^{2} - 19 x - 7$ .

(b) using the FOIL method $(3 x + 1) (2 x - 7) = 6 x^{2} - 19 x - 7$ .

(c) Using the Vertical method $(3 x + 1) (2 x - 7) = 6 x^{2} - 19 x - 7$ .

Step by step solution

01

Step 1

(a) Use the distributive property $a (b + c) = a 路 b + a 路 c$ as follows:

$\begin{array}{rcl} (3 x + 1) (2 x - 7) & = & 3 x (2 x - 7) + 1 (2 x - 7) \\ = & (3 x) (2 x) + (3 x) (- 7) + 1 (2 x) + 1 (- 7) \\ = & 6 x^{2} - 21 x + 2 x - 7 \\ (3 x + 1) (2 x - 7) & = & 6 x^{2} - 19 x - 7 \end{array}$

02

Step 2

(b) Use the FOIL method to multiply the binomials $(3 x + 1) (2 x - 7)$ .

Multiply First terms $3 x, 2 x$ : $3 x 路 2 x = 6 x^{2}$ .

Multiply Outer terms $3 x, - 7$ : $3 x (- 7) = - 21 x$ .

Multiply Inner terms $1, 2 x$ : $1 路 2 x = 2 x$ .

Multiply Last terms $1, - 7$ : $1 (- 7) = - 7$ .

Finally, add the terms:

$\begin{array}{rcl} (3 x + 1) (2 x - 7) & = & 6 x^{2} - 21 x + 2 x - 7 \\ = & 6 x^{2} - 19 x - 7 \end{array}$

So, $(3 x + 1) (2 x - 7) = 6 x^{2} - 19 x - 7$ .

03

Step 3

(c) Use the vertical method.

$3 x + 1 脳 2 x - 7 - 21 x - 7 6 x^{2} + 2 x 6 x^{2} - 19 x - 7$

So, $(3 x + 1) (2 x - 7) = 6 x^{2} - 19 x - 7$ .

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