Pre-Algebra Examples

$\frac{3}{4} x^{4} + 19 x^{3} + \frac{1}{8} x^{4} - 20 x^{3} - 17$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $\frac{3}{4}$ and $x^{4}$ .

$\frac{3 x^{4}}{4} + 19 x^{3} + \frac{1}{8} x^{4} - 20 x^{3} - 17$

Step 1.2

Combine $\frac{1}{8}$ and $x^{4}$ .

$\frac{3 x^{4}}{4} + 19 x^{3} + \frac{x^{4}}{8} - 20 x^{3} - 17$

Step 2

Find the common denominator.

Tap for more steps...

Step 2.1

Multiply $\frac{3 x^{4}}{4}$ by $\frac{2}{2}$ .

$\frac{3 x^{4}}{4} \cdot \frac{2}{2} + 19 x^{3} + \frac{x^{4}}{8} - 20 x^{3} - 17$

Step 2.2

Multiply $\frac{3 x^{4}}{4}$ by $\frac{2}{2}$ .

$\frac{3 x^{4} \cdot 2}{4 \cdot 2} + 19 x^{3} + \frac{x^{4}}{8} - 20 x^{3} - 17$

Step 2.3

Write $19 x^{3}$ as a fraction with denominator $1$ .

$\frac{3 x^{4} \cdot 2}{4 \cdot 2} + \frac{19 x^{3}}{1} + \frac{x^{4}}{8} - 20 x^{3} - 17$

Step 2.4

Multiply $\frac{19 x^{3}}{1}$ by $\frac{8}{8}$ .

$\frac{3 x^{4} \cdot 2}{4 \cdot 2} + \frac{19 x^{3}}{1} \cdot \frac{8}{8} + \frac{x^{4}}{8} - 20 x^{3} - 17$

Step 2.5

Multiply $\frac{19 x^{3}}{1}$ by $\frac{8}{8}$ .

$\frac{3 x^{4} \cdot 2}{4 \cdot 2} + \frac{19 x^{3} \cdot 8}{8} + \frac{x^{4}}{8} - 20 x^{3} - 17$

Step 2.6

Write $- 20 x^{3}$ as a fraction with denominator $1$ .

$\frac{3 x^{4} \cdot 2}{4 \cdot 2} + \frac{19 x^{3} \cdot 8}{8} + \frac{x^{4}}{8} + \frac{- 20 x^{3}}{1} - 17$

Step 2.7

Multiply $\frac{- 20 x^{3}}{1}$ by $\frac{8}{8}$ .

$\frac{3 x^{4} \cdot 2}{4 \cdot 2} + \frac{19 x^{3} \cdot 8}{8} + \frac{x^{4}}{8} + \frac{- 20 x^{3}}{1} \cdot \frac{8}{8} - 17$

Step 2.8

Multiply $\frac{- 20 x^{3}}{1}$ by $\frac{8}{8}$ .

$\frac{3 x^{4} \cdot 2}{4 \cdot 2} + \frac{19 x^{3} \cdot 8}{8} + \frac{x^{4}}{8} + \frac{- 20 x^{3} \cdot 8}{8} - 17$

Step 2.9

Write $- 17$ as a fraction with denominator $1$ .

$\frac{3 x^{4} \cdot 2}{4 \cdot 2} + \frac{19 x^{3} \cdot 8}{8} + \frac{x^{4}}{8} + \frac{- 20 x^{3} \cdot 8}{8} + \frac{- 17}{1}$

Step 2.10

Multiply $\frac{- 17}{1}$ by $\frac{8}{8}$ .

$\frac{3 x^{4} \cdot 2}{4 \cdot 2} + \frac{19 x^{3} \cdot 8}{8} + \frac{x^{4}}{8} + \frac{- 20 x^{3} \cdot 8}{8} + \frac{- 17}{1} \cdot \frac{8}{8}$

Step 2.11

Multiply $\frac{- 17}{1}$ by $\frac{8}{8}$ .

$\frac{3 x^{4} \cdot 2}{4 \cdot 2} + \frac{19 x^{3} \cdot 8}{8} + \frac{x^{4}}{8} + \frac{- 20 x^{3} \cdot 8}{8} + \frac{- 17 \cdot 8}{8}$

Step 2.12

Reorder the factors of $4 \cdot 2$ .

$\frac{3 x^{4} \cdot 2}{2 \cdot 4} + \frac{19 x^{3} \cdot 8}{8} + \frac{x^{4}}{8} + \frac{- 20 x^{3} \cdot 8}{8} + \frac{- 17 \cdot 8}{8}$

Step 2.13

Multiply $2$ by $4$ .

$\frac{3 x^{4} \cdot 2}{8} + \frac{19 x^{3} \cdot 8}{8} + \frac{x^{4}}{8} + \frac{- 20 x^{3} \cdot 8}{8} + \frac{- 17 \cdot 8}{8}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 x^{4} \cdot 2 + 19 x^{3} \cdot 8 + x^{4} - 20 x^{3} \cdot 8 - 17 \cdot 8}{8}$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Multiply $2$ by $3$ .

$\frac{6 x^{4} + 19 x^{3} \cdot 8 + x^{4} - 20 x^{3} \cdot 8 - 17 \cdot 8}{8}$

Step 4.2

Multiply $8$ by $19$ .

$\frac{6 x^{4} + 152 x^{3} + x^{4} - 20 x^{3} \cdot 8 - 17 \cdot 8}{8}$

Step 4.3

Multiply $8$ by $- 20$ .

$\frac{6 x^{4} + 152 x^{3} + x^{4} - 160 x^{3} - 17 \cdot 8}{8}$

Step 4.4

Multiply $- 17$ by $8$ .

$\frac{6 x^{4} + 152 x^{3} + x^{4} - 160 x^{3} - 136}{8}$

Step 5

Simplify by adding terms.

Tap for more steps...

Step 5.1

Add $6 x^{4}$ and $x^{4}$ .

$\frac{7 x^{4} + 152 x^{3} - 160 x^{3} - 136}{8}$

Step 5.2

Subtract $160 x^{3}$ from $152 x^{3}$ .

$\frac{7 x^{4} - 8 x^{3} - 136}{8}$