# What is 3x 8y+4x+2y

## Final result :

3y • (2x4 + x3y - 4xy + 8y2) ———————————————————————————— 4x

## Step  1  :

3x - 6y Simplify ——————— x

## Step  2  :

#### Pulling out like terms :

2.1     Pull out like factors :

3x - 6y  =   3 • (x - 2y)

#### Equation at the end of step  2  :

(6x+3y) 3•(x-2y) ((———————•(x2))•y)-(————————•y2) 4 x

## Step  3  :

#### Equation at the end of step  3  :

(6x+3y) 3y2•(x-2y) ((———————•(x2))•y)-—————————— 4 x

## Step  4  :

6x + 3y Simplify ——————— 4

## Step  5  :

#### Pulling out like terms :

5.1     Pull out like factors :

6x + 3y  =   3 • (2x + y)

#### Equation at the end of step  5  :

3•(2x+y) 3y2•(x-2y) ((————————•x2)•y)-—————————— 4 x

## Step  6  :

#### Equation at the end of step  6  :

3x2 • (2x + y) 3y2 • (x - 2y) (—————————————— • y) - —————————————— 4 x

## Step  7  :

#### Equation at the end of step  7  :

3x2y • (2x + y) 3y2 • (x - 2y) ——————————————— - —————————————— 4 x

## Step  8  :

#### Calculating the Least Common Multiple :

8.1    Find the Least Common Multiple

The left denominator is :       4

The right denominator is :       x

Prime
Factor
Left
Denominator
Right
Denominator
L.C.M = Max
{Left,Right}
2202
Product of all
Prime Factors
414
Algebraic
Factor
Left
Denominator
Right
Denominator
L.C.M = Max
{Left,Right}
x 011

Least Common Multiple:
4x

#### Calculating Multipliers :

8.2    Calculate multipliers for the two fractions

Denote the Least Common Multiple by  L.C.M
Denote the Left Multiplier by  Left_M
Denote the Right Multiplier by  Right_M
Denote the Left Deniminator by  L_Deno
Denote the Right Multiplier by  R_Deno

Left_M = L.C.M / L_Deno = x

Right_M = L.C.M / R_Deno = 4

#### Making Equivalent Fractions :

8.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 3x2y • (2x+y) • x —————————————————— = ————————————————— L.C.M 4x R. Mult. • R. Num. 3y2 • (x-2y) • 4 —————————————————— = ———————————————— L.C.M 4x

#### Adding fractions that have a common denominator :

8.4       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3x2y • (2x+y) • x - (3y2 • (x-2y) • 4) 6x4y + 3x3y2 - 12xy2 + 24y3 —————————————————————————————————————— = ——————————————————————————— 4x 4x

## Step  9  :

#### Pulling out like terms :

9.1     Pull out like factors :

6x4y + 3x3y2 - 12xy2 + 24y3  =

3y • (2x4 + x3y - 4xy + 8y2

#### Checking for a perfect cube :

9.2    2x4 + x3y - 4xy + 8y2  is not a perfect cube

## Final result :

3y • (2x4 + x3y - 4xy + 8y2) ———————————————————————————— 4x

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