Chapter 5: Q. 185 (page 536)

In the following exercises, multiply.
$(a) - 5 m (m^{2} + 3 m - 18) (b) - 3 x^{2} y^{2} (7 x^{2} + 10 x y - y^{2})$

Short Answer

Expert verified

The solution is

$(a) - 5 m (m^{2} + 3 m - 18) = - 5 m^{3} - 15 m^{2} + 90 m (b) - 3 x^{2} y^{2} (7 x^{2} + 10 x y - y^{2}) = - 21 x^{4} y^{2} - 30 x^{3} y^{3} + 3 x^{2} y^{4}$

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

$- 5 m (m^{2} + 3 m - 18)$

Part (a) Step 2. Simplify

Using the Distributive property,

$- 5 m (m^{2} + 3 m - 18) = - 5 m \cdot m^{2} - 5 m \cdot 3 m + 5 m \cdot 18 = - 5 m^{3} - 15 m^{2} + 90 m$

Part (b) Step 1. Given expression

The given expression is

$- 3 x^{2} y^{2} (7 x^{2} + 10 x y - y^{2})$

Part (b) Step 2. Simplify

Using Distributive property,

$- 3 x^{2} y^{2} (7 x^{2} + 10 x y - y^{2}) = - 3 x^{2} y^{2} \cdot 7 x^{2} - 3 x^{2} y^{2} \cdot 10 x y + 3 x^{2} y^{2} \cdot y^{2} = - 21 x^{4} y^{2} - 30 x^{3} y^{3} + 3 x^{2} y^{4}$

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In the following exercises, multiply.
$(a) - 5 m (m^{2} + 3 m - 18) (b) - 3 x^{2} y^{2} (7 x^{2} + 10 x y - y^{2})$

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 expression

Part (b) Step 2. Simplify

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In the following exercises, multiply.a-5mm2+3m-18b-3x2y27x2+10xy-y2

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 expression

Part (b) Step 2. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, multiply.
$(a) - 5 m (m^{2} + 3 m - 18) (b) - 3 x^{2} y^{2} (7 x^{2} + 10 x y - y^{2})$