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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 71 E (page 885)

Completing the square of a binomial expression .
In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
(a) $m^{2} - 24 m$
(b) $x^{2} - 11 x$
(c) $p^{2} - \frac{1}{3} p$

Short Answer

Expert verified

The binomial squared expression is

(a) ${(m - 12)}^{2}$

(b) ${(x - \frac{11}{2})}^{2}$

(c) ${(p - \frac{1}{6})}^{2}$

Step by step solution

01

(a) Step 1: Given information

$m^{2} - 24 m$

02

(a) Step 2: Calculation

$m^{2} - 24 m = m^{2} - 24 m + (\frac{1}{2} 脳 {(- 24))}^{2} = m^{2} - 24 m + 144 = {(m - 12)}^{2}$

03

(b) Step 1: Given information

$x^{2} - 11 x$

04

(b) Step 2: Calculation

$x^{2} - 11 x = x^{2} - 11 x + (\frac{1}{2} 脳 {(- 11))}^{2} = x^{2} - 11 x + \frac{121}{4} = {(x - \frac{11}{2})}^{2}$

05

(c) Step 1 : Given information

$p^{2} - \frac{1}{3} p$

06

(c) Step 2: Calculation

$p^{2} - \frac{1}{3} p = p^{2} - \frac{1}{3} p + (\frac{1}{2} 脳 {(\frac{- 1}{3}))}^{2} = p^{2} - \frac{1}{3} p + \frac{1}{36} = {(p - \frac{1}{6})}^{2}$

The binomial squared expression is

(a) ${(m - 12)}^{2}$

(b) ${(x - \frac{11}{2})}^{2}$

(c) ${(p - \frac{1}{6})}^{2}$

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