Question

Simplify: 2/5 (10x − 10y) − 3/4(12x − 24y)

Answer 1

14y - 5x

Explanation:

Step 1 :

3

Simplify —

4

Equation at the end of step 1 :

2 3

(— • (10x - 10y)) - (— • (12x - 24y))

5 4

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

12x - 24y = 12 • (x - 2y)

Equation at the end of step 3 :

2

(— • (10x - 10y)) - 9 • (x - 2y)

5

Step 4 :

2

Simplify —

5

Equation at the end of step 4 :

2

(— • (10x - 10y)) - 9 • (x - 2y)

5

Step 5 :

Step 6 :

Pulling out like terms :

6.1 Pull out like factors :

10x - 10y = 10 • (x - y)

Equation at the end of step 6 :

4 • (x - y) - 9 • (x - 2y)

Step 7 :

Final result :

14y - 5x

Answer 2

-5x + 14y

Explanation:

`(2)/(5) (10x-10y)-(3)/(4) (12x-24y)`

`(2)/(5) (10x-10y)`

Multiply fractions:
`a*(b)/(c) =(a*b)/(c)`

`=(2(10x-10y))/(5)`

Factor 2 ( 10x - 10y)

`=(20(x-y))/(5)`

Divide the numbers:
`(20)/(5) =4`

= 4 ( x - y )

`(3)/(4) (12x-24y)=9(x-2y)`

`(3)/(4) (12x-24y)`

Multiply fractions:
`a*(b)/(c) =(a*b)/(c)`

`=(3(12x-24y))/(4)`

Factor 3 ( 12x - 24y )

3 ( 12x - 24 )

Factor 12x - 24y

`=3*12(x-2y)`

Refine.

`=36(x-2y)`

`=(36(x-2y))/(4)`

Divide the numbers:
`(36)/(4) =9`

`=9(x-2y)`

`=4x-4y-9(x-2y)`

Expand
`-9(x-2y)`

`-9(x-2y)`

Apply the distributive law:
`a(b-c)=ab-ac`

`a=-9, b= x, c= 2y`

= 9x - ( - 9 ) * 2y

= -9x + 9 * 2y

= 9x + 18y

Simplify 4x-4y-9x+18y

4x-4y-9x+18y

Group like terms.

=4x-9x-4y+18y

Add similar elements: 4x - 9x =-5x

Add similar elements: -4y +18y = 14y

= -5x +14y