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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. 9.21TI (page 875)

Complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
$a a^{2} - 20 a$ $b m^{2} - 5 m$ $c p^{2} + \frac{1}{4} p$

Short Answer

Expert verified

The solution is $a {(a - 10)}^{2}$ , $b {(m - \frac{5}{2})}^{2}$ , $c {(p + \frac{1}{8})}^{2}$

Step by step solution

01

Part (a) Step 1. Given information

Expression: $a^{2} - 20 a$

02

Part (a) Step 2. Calculation

We have,

$a^{2} - 20 a$

The coefficient of $a$ is $- 20$ .

Now, ${(\frac{1}{2} 路 (- 20))}^{2}$

role="math" localid="1645033170915" $= {(- 10)}^{2}$

$= 100$

So, role="math" localid="1645034017935" $a^{2} - 20 a + 100 = {(a - 10)}^{2}$

03

Part (b) Step 1. Given information

Expression: $m^{2} - 5 m$

04

Part (b) Step 2. Calculation

We have,

$m^{2} - 5 m$

The coefficient of $m$ is $- 5$ .

Now, ${(\frac{1}{2} 路 (- 5))}^{2}$

role="math" localid="1645033844110" $= {(\frac{- 5}{2})}^{2}$

$= \frac{25}{4}$

So, role="math" localid="1645034070399" $m^{2} - 5 m + \frac{25}{4} = {(m - \frac{5}{2})}^{2}$

05

Part (c) Step 1. Given information

Expression: $p^{2} + \frac{1}{4} p$

06

Part (c) Step 2. Calculation

We have,

$p^{2} + \frac{1}{4} p$

The coefficient of $p$ is $\frac{1}{4}$ .

Now, ${(\frac{1}{2} 路 (\frac{1}{4}))}^{2}$

$= {(\frac{1}{8})}^{2}$

$= \frac{1}{64}$

So, $p^{2} + \frac{1}{4} p + \frac{1}{64} = {(p + \frac{1}{8})}^{2}$

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