Chapter 1: Q10. (page 18)

Simplify $4 (14 x - 10 y) - 6 (x + 4 y)$

Short Answer

Expert verified

$4 (14 x - 10 y) - 6 (x + 4 y)$ is simplified to $2 (25 x - 32 y)$

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, first use distributive property then commutative property of addition then distributive property to group coefficients of same variable as shown below
$\begin{matrix} 4 (14 x - 10 y) - 6 (x + 4 y) = 56 x - 40 y - 6 x - 24 y \\ = 56 x - 6 x - 40 y - 24 y \\ = (56 - 6) x - (40 + 24) y \end{matrix}$

- Use distributive property

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

$\begin{matrix} (56 - 6) x - (40 + 24) y = 50 x - 64 y \\ = 2 (25 x - 32 y) \end{matrix}$

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Simplify $4 (14 x - 10 y) - 6 (x + 4 y)$

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Use distributive property

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Simplify 414x-10y-6x+4y

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

Applied Mathematics

Probability and Statistics

Geometry

Theoretical and Mathematical Physics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Simplify $4 (14 x - 10 y) - 6 (x + 4 y)$