Q54. Simplify each expression414c-10d... [FREE SOLUTION]

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Chapter 1: Q54. (page 16)

Simplify each expression
$4 (14 c - 10 d) - 6 (d + 4 c)$

Short Answer

Expert verified

$4 (14 c - 10 d) - 6 (d + 4 c)$ is simplified to $2 (16 c - 23 d)$

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	$a 路 b = b 路 a$
Associative	$(a + b) + c = a + (b + c)$	$(a 路 b) 路 c = a 路 (b 路 c)$
Identity	a+0=a=0+a	$a 路 1 = a = 1 路 a$
Inverse	$a + (- a) = 0 = (- a) + a$	If $a 鈮� 0$ , then $a 路 \frac{1}{a} = 1 = \frac{1}{a} 路 a$
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, first use distributive property then commutative property of addition then distributive property to group coefficients of same variable as shown below

$\begin{matrix} 4 (14 c 鈭� 10 d) 鈭� 6 (d + 4 c) = 56 c 鈭� 40 d 鈭� 6 d 鈭� 24 c \\ = 56 c 鈭� 40 d 鈭� 24 c 鈭� 6 d \\ = 56 c 鈭� 24 c 鈭� 40 d 鈭� 6 d \\ = (56 鈭� 24) c 鈭� (40 + 6) d \end{matrix}$

- Use distributive property

Firstly simplify parentheses then take out common factor of both terms as shown below

$\begin{matrix} (56 鈭� 24) c 鈭� (40 + 6) d = 32 c 鈭� 46 d \\ = 2 (16 c 鈭� 23 d) \end{matrix}$

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91影视

Simplify each expression
$4 (14 c - 10 d) - 6 (d + 4 c)$

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Use distributive property

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91影视

Simplify each expression414c-10d-6d+4c

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Use distributive property

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Statistics

Decision Maths

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Simplify each expression
$4 (14 c - 10 d) - 6 (d + 4 c)$