Chapter 6: Q. 6.9 (page 569)

Factor: $- 4 b^{3} + 16 b^{2} - 8 b$

Short Answer

Expert verified

The factored form is $\begin{array}{rcl} - 4 b (b^{2} - b + 2) \end{array}$ .

Step by step solution

Step 1. Given information

The given expression is $- 4 b^{3} + 16 b^{2} - 8 b$ .

Step 2. Rewrite the given expression

Express each of the term of the given expression as a product of GCF, $- 4 b$ .

$- 4 b \cdot b^{2} - (- 4 b) \cdot b + (- 4 b) \cdot 2$

Use the reverse distributive property, $a b + a c = a (b + c)$ to rewrite the obtained expression.

role="math" localid="1644852269198" $- 4 b \cdot b^{2} - (- 4 b) \cdot b + (- 4 b) \cdot 2 = - 4 b (b^{2} - b + 2)$

Step 3. Check

Multiply the obtained factors.

$\begin{array}{rcl} - 4 b (b^{2} - b + 2) & = & - 4 b \cdot b^{2} - (- 4 b) \cdot b + (- 4 b) \cdot 2 \\ = & - 4 b^{3} + 4 b^{2} - 8 b \end{array}$

Since the obtained expression is the same as the given expression, the obtained factors are verified.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Factor: $- 4 b^{3} + 16 b^{2} - 8 b$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rewrite the given expression

Step 3. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Factor:-4b3+16b2-8b

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rewrite the given expression

Step 3. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Factor: $- 4 b^{3} + 16 b^{2} - 8 b$