Q10. Simplify 414x-10y-6x+4y... [FREE SOLUTION]

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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	$a + b = b + a$	$a 路 b = b 路 a$
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
$\begin{matrix} 4 (14 x 鈭� 10 y) 鈭� 6 (x + 4 y) = 56 x 鈭� 40 y 鈭� 6 x 鈭� 24 y \\ = 56 x 鈭� 6 x 鈭� 40 y 鈭� 24 y \\ = (56 鈭� 6) x 鈭� (40 + 24) y \end{matrix}$

- Use distributive property

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

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

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91影视

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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