Chapter 5: Q. 182 (page 536)

In the following exercises, multiply.
$(a) - 8 x (x^{2} + 2 x - 15) (b) 5 p q^{3} (p^{2} - 2 p q + 6 q^{2})$

Short Answer

Expert verified

The solution is

$(a) - 8 x (x^{2} + 2 x - 15) = - 8 x^{3} - 16 x^{2} + 120 x (b) 5 p q^{3} (p^{2} - 2 p q + 6 q^{2}) = 5 p^{3} q^{3} - 10 p^{2} q^{4} + 30 p q^{5}$

Step by step solution

Step 1. Apply the concept of Distributive Property

If $A, B, C$ are any real number or algebraic expressions then

$A (B + C) = (B + C) A = A B + A C$

Part (a) Step 1. Given expression

The given expression is

$- 8 x (x^{2} + 2 x - 15)$

Part (a) Step 2. Simplify

Using Distributive property ,

$- 8 x (x^{2} + 2 x - 15) = (- 8 x) \cdot x^{2} - 16 x \cdot x + 120 x = - 8 x^{3} - 16 x^{2} + 120 x$

Part (b) Step 1. Given information

The given expression is

$5 p q^{3} (p^{2} - 2 p q + 6 q^{2})$

Part (b) Step 2. Simplify

Using Distributive property,

$5 p q^{3} (p^{2} - 2 p q + 6 q^{2}) = 5 p q^{3} \cdot p^{2} - 5 p q^{3} \cdot 2 p q + 5 p q^{3} \cdot 6 q^{2} = 5 p^{3} q^{3} - 10 p^{2} q^{4} + 30 p q^{5}$

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.

In the following exercises, multiply.
$(a) - 8 x (x^{2} + 2 x - 15) (b) 5 p q^{3} (p^{2} - 2 p q + 6 q^{2})$

Short Answer

Step by step solution

Step 1. Apply the concept of Distributive Property

Part (a) Step 1. Given expression

Part (a) Step 2. Simplify

Part (b) Step 1. Given information

Part (b) Step 2. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, multiply.a-8xx2+2x-15b5pq3p2-2pq+6q2

Short Answer

Step by step solution

Step 1. Apply the concept of Distributive Property

Part (a) Step 1. Given expression

Part (a) Step 2. Simplify

Part (b) Step 1. Given information

Part (b) Step 2. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, multiply.
$(a) - 8 x (x^{2} + 2 x - 15) (b) 5 p q^{3} (p^{2} - 2 p q + 6 q^{2})$