Chapter 1: Q15. (page 15)

Simplify each expression
$3 (5 c + 4 d) + 6 (d - 2 c)$

Short Answer

Expert verified

$3 (5 c + 4 d) + 6 (d - 2 c)$ is simplified to $3 (c + 6 d)$

Step by step solution

- Write properties of real numbers

Properties of real numbers are written in following table:

For any real numbers $a, b,$ and $c :$
Property	Addition	Multiplication
Commutative	$a + b = b + a$	$a \cdot b = b \cdot a$
Associative	$(a + b) + c = a + (b + c)$	$(a \cdot b) \cdot c = a \cdot (b \cdot c)$
Identity	$a + 0 = a = 0 + a$	$a \cdot 1 = a = 1 \cdot a$
Inverse	$a + (- a) = 0 = (- a) + a$	If $a \neq 0$ , then $a \cdot \frac{1}{a} = 1 = \frac{1}{a} \cdot a$
Distributive	$a (b + c) = a b + a c and (b + c) a = b a + c a$

- Simplify by grouping same variables

To simplify given equation, use commutative and distributive property to group coefficients of same variable as shown below

$\begin{matrix} 3 (5 c + 4 d) + 6 (d - 2 c) = 15 c + 12 d + 6 d - 12 c \\ = 15 c + 12 d - 12 c + 6 d \\ = 15 c - 12 c + 12 d + 6 d \\ = (15 - 12) c + (12 + 6) d \end{matrix}$

- Simplify parentheses

Simplify parentheses by adding the terms then use distributive property to take out common factor as shown below

$\begin{matrix} (15 - 12) c + (12 + 6) d = 3 c + 18 d \\ = 3 (c + 6 d) \end{matrix}$

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Simplify each expression
$3 (5 c + 4 d) + 6 (d - 2 c)$

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Simplify parentheses

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Simplify each expression35c+4d+6d-2c

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Simplify parentheses

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Calculus

Geometry

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Simplify each expression
$3 (5 c + 4 d) + 6 (d - 2 c)$