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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. 186 (page 536)

In the following exercises, multiply the binomials using
(a) the Distributive Property;
(b) the FOIL method;
(c) the Vertical Method.
$(w + 5) (w + 7)$

Short Answer

Expert verified

The solution is

$(w + 5) (w + 7) = w^{2} + 12 w + 35$

Step by step solution

01

Step 1. Given expression

The given expression is

$(w + 5) (w + 7)$

02

Part (a) Step 1. Apply the concept of Distributive property

are any real numbers or algebraic expressions, then

$(A + B) (C + D) = A (C + D) + B (C + D) = A C + A D + B C + B D$

03

Part (a) Step 2. Simplify using Distributive property

Using Distributive property, $(w + 5) (w + 7) = w (w + 7) + 5 (w + 7) = w^{2} + 7 w + 5 w + 35 = w^{2} + 12 w + 35$

04

Part (b) Step 1. Apply the concept of Foil method

If $A, B, C a n d D$ are any algebraic expressions then, $(A + B) (C + D)$ can be simplified by Foil property using following steps

Multiply the First terms $A$ and $C$
Multiply the Outer Terms $A a n d D$
Multiply the last terms $B a n d D$
Combine like terms, when possible

05

Part (b) Step 2. Simplify using Foil method

Using Foil method,

(w + 5) (w + 7)

$(w + 5) (w + 7) = w^{2} +_+_+_$
$(w + 5) (w + 7) = w^{2} + 7 w +_+_$
$(w + 5) (w + 7) = w^{2} + 7 w + 5 w +_$
$(w + 5) (w + 7) = w^{2} + 7 w + 5 w + 35$
$(w + 5) (w + 7) = w^{2} + 12 w + 35$

06

Part (c) Step 1. Apply the concept of Vertical method

To multiply two polynomials we use vertical method

07

Part (c) Step 2. Simplify using vertical method

Using vertical method,

$w + 5 \frac{脳 w + 7}{7 w + 35} p a r t i a l p r o d u c t \frac{w^{2} + 5 w}{w^{2} + 12 w + 35} p a r t i a l p r o d u c t$

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