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

Step 1. Given information.

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

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 $- 8$ .

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 $16$ .

Step 4. Now, complete the square.

Add $16$ to the given binomial expression.

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

Step 5. Simplified answer.

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

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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

Step by step solution

Step 1. Given information.

Step 2. Identify b, the coefficient of m.

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

Step 4. Now, complete the square.

Step 5. Simplified answer.

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In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.m2-8m

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Identify b, the coefficient of m.

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

Step 4. Now, complete the square.

Step 5. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Applied Mathematics

Decision Maths

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

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