Chapter 9: Q.414. (page 982)

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
$b^{2} + 13 b$

Short Answer

Expert verified

The solution is ${(b + \frac{13}{2})}^{2}$ .

Step by step solution

Step 1. Given information.

The given binomial expression is $b^{2} + 13 b$ .

Step 2. Identify the coefficient of b.

Comparing the given binomial expression with $b^{2} + a b$ .

We have $a = 13$ .

So, the coefficient of $b$ is $13$ .

Step 3. Find the number to complete the square.

$\begin{array}{rcl} {(\frac{1}{2} a)}^{2} & = & {(\frac{1}{2} \cdot 13)}^{2} \\ = & \frac{169}{4} \end{array}$

Step 4. Now complete the square.

Add $\frac{169}{4}$ to the given binomial expression.

$\begin{array}{rcl} b^{2} + 13 b + \frac{169}{4} & = & b^{2} + 2 \cdot b \cdot \frac{13}{2} + {(\frac{13}{2})}^{2} \\ = & {(b + \frac{13}{2})}^{2} \end{array}$

Step 5. Simplified answer.

Hence, the required complete square trinomial is $\begin{array}{rcl} {(b + \frac{13}{2})}^{2} \end{array}$ .

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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.
$b^{2} + 13 b$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Identify the coefficient of b.

Step 3. Find 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.b2+13b

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Identify the coefficient of b.

Step 3. Find 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

Discrete Mathematics

Probability and Statistics

Logic and Functions

Geometry

Pure Maths

Calculus

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.
$b^{2} + 13 b$