Chapter 5: Q. 184 (page 536)

In the following exercises, multiply.
$(a) - 8 y (y^{2} + 2 y - 15) (b) - 4 y^{2} z^{3} (3 y^{2} + 12 y z - z^{2})$

Short Answer

Expert verified

The solution is

$(a) - 8 y (y^{2} + 2 y - 15) = - 8 y^{3} - 16 y^{2} + 120 y (b) - 4 y^{2} z^{3} (3 y^{2} + 12 y z - z^{2}) = - 12 y^{4} z^{3} - 48 y^{3} z^{4} + 4 y^{2} z^{5}$

Step by step solution

Step 1. Apply the concept of Distributive Property

If $A, B a n d C$ are any real numbers or algebraic expressions, then

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

Part (a) Step 1. Given information

The given expression is

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

Part (a) Step 2. Simplify

Using Distributive property,

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

Part (b) Step 1. Given information

The given expression is

$- 4 y^{2} z^{3} (3 y^{2} + 12 y z - z^{2})$

Part (b) Step 2. Simplify

Using Distributive property,

$- 4 y^{2} z^{3} (3 y^{2} + 12 y z - z^{2}) = - 4 y^{2} z^{3} \cdot 3 y^{2} - 4 y^{2} z^{3} \cdot 12 y z + 4 y^{2} z^{3} \cdot z^{2} = - 12 y^{4} z^{3} - 48 y^{3} z^{4} + 4 y^{2} z^{5}$

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In the following exercises, multiply.
$(a) - 8 y (y^{2} + 2 y - 15) (b) - 4 y^{2} z^{3} (3 y^{2} + 12 y z - z^{2})$

Short Answer

Step by step solution

Step 1. Apply the concept of Distributive Property

Part (a) Step 1. Given information

Part (a) Step 2. Simplify

Part (b) Step 1. Given information

Part (b) Step 2. Simplify

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In the following exercises, multiply.a-8yy2+2y-15b-4y2z33y2+12yz-z2

Short Answer

Step by step solution

Step 1. Apply the concept of Distributive Property

Part (a) Step 1. Given information

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

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Discrete Mathematics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, multiply.
$(a) - 8 y (y^{2} + 2 y - 15) (b) - 4 y^{2} z^{3} (3 y^{2} + 12 y z - z^{2})$