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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.412. (page 982)

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
$m^{2} - 8 m$

Short Answer

Expert verified

The solution is ${(m - 4)}^{2}$ .

Step by step solution

01

Step 1. Given information.

The given expression is $m^{2} - 8 m$ .

02

Step 2. Identify b, the coefficient of m.

The given binomial expression is $m^{2} - 8 m$ .

Comparing given expression with $m^{2} + b m$ , we have $b = - 8$ .

Thus, the coefficient of $m$ is $- 8$ .

03

Step 3. Find 12b2, the number to complete the square.

$\begin{array}{rcl} {(\frac{1}{2} b)}^{2} & = & {(\frac{1}{2} (- 8))}^{2} \\ = & {(- 4)}^{2} \\ = & 16 \end{array}$

Thus, the number to complete the square is $16$ .

04

Step 4. Now, complete the square.

Add $16$ to the given binomial expression.

$\begin{array}{rcl} m^{2} - 8 m + 16 & = & m^{2} - 2 路 m 路 4 + {(4)}^{2} \\ = & {(m - 4)}^{2} \end{array}$

05

Step 5. Simplified answer.

Hence, the required trinomial is ${(m - 4)}^{2}$ .

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Most popular questions from this chapter

John has a 10-foot piece of rope that he wants to use to support his 8-foot tree. How far from the base of the tree should he secure the rope?

In the following exercise, solve by completing the square.

$x^{2} - 20 x = 21$

In the following exercises, solve by using the Quadratic Formula.
$25 d^{2} - 60 d + 36 = 0$

In the following exercises, solve by using the Quadratic Formula.
$(x + 2) (x + 6) = 21$

Use the Discriminant to Predict the Number of Solutions of a Quadratic Equation.

In the following exercises, determine the number of solutions for each quadratic equation.

$(a) 9 v^{2} - 15 v + 25 = 0 (b) 100 w^{2} + 60 w + 9 = 0 (c) 5 c^{2} + 7 c - 10 = 0$

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