Algebra Examples

$(\frac{1}{2} x^{3} + y^{4}) + (\frac{3}{2} x^{4} y^{3} - \frac{11}{4} x^{3} + \frac{5}{2} y^{4})$

Step 1

Remove parentheses.

$\frac{1}{2} x^{3} + y^{4} + \frac{3}{2} \cdot (x^{4} y^{3}) - \frac{11}{4} x^{3} + \frac{5}{2} y^{4}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Combine $\frac{1}{2}$ and $x^{3}$ .

$\frac{x^{3}}{2} + y^{4} + \frac{3}{2} \cdot (x^{4} y^{3}) - \frac{11}{4} x^{3} + \frac{5}{2} y^{4}$

Step 2.2

Multiply $\frac{3}{2} (x^{4} y^{3})$ .

Tap for more steps...

Step 2.2.1

Combine $x^{4}$ and $\frac{3}{2}$ .

$\frac{x^{3}}{2} + y^{4} + \frac{x^{4} \cdot 3}{2} y^{3} - \frac{11}{4} x^{3} + \frac{5}{2} y^{4}$

Step 2.2.2

Combine $\frac{x^{4} \cdot 3}{2}$ and $y^{3}$ .

$\frac{x^{3}}{2} + y^{4} + \frac{x^{4} \cdot 3 y^{3}}{2} - \frac{11}{4} x^{3} + \frac{5}{2} y^{4}$

Step 2.3

Move $3$ to the left of $x^{4}$ .

$\frac{x^{3}}{2} + y^{4} + \frac{3 \cdot x^{4} y^{3}}{2} - \frac{11}{4} x^{3} + \frac{5}{2} y^{4}$

Step 2.4

Combine $x^{3}$ and $\frac{11}{4}$ .

$\frac{x^{3}}{2} + y^{4} + \frac{3 x^{4} y^{3}}{2} - \frac{x^{3} \cdot 11}{4} + \frac{5}{2} y^{4}$

Step 2.5

Move $11$ to the left of $x^{3}$ .

$\frac{x^{3}}{2} + y^{4} + \frac{3 x^{4} y^{3}}{2} - \frac{11 \cdot x^{3}}{4} + \frac{5}{2} y^{4}$

Step 2.6

Combine $\frac{5}{2}$ and $y^{4}$ .

$\frac{x^{3}}{2} + y^{4} + \frac{3 x^{4} y^{3}}{2} - \frac{11 x^{3}}{4} + \frac{5 y^{4}}{2}$

Step 3

To write $\frac{x^{3}}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y^{4} + \frac{3 x^{4} y^{3}}{2} + \frac{x^{3}}{2} \cdot \frac{2}{2} - \frac{11 x^{3}}{4} + \frac{5 y^{4}}{2}$

Step 4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

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

$y^{4} + \frac{3 x^{4} y^{3}}{2} + \frac{x^{3} \cdot 2}{2 \cdot 2} - \frac{11 x^{3}}{4} + \frac{5 y^{4}}{2}$

Step 4.2

Multiply $2$ by $2$ .

$y^{4} + \frac{3 x^{4} y^{3}}{2} + \frac{x^{3} \cdot 2}{4} - \frac{11 x^{3}}{4} + \frac{5 y^{4}}{2}$

Step 5

Combine the numerators over the common denominator.

$y^{4} + \frac{3 x^{4} y^{3}}{2} + \frac{x^{3} \cdot 2 - 11 x^{3}}{4} + \frac{5 y^{4}}{2}$

Step 6

Subtract $11 x^{3}$ from $x^{3} \cdot 2$ .

Tap for more steps...

Step 6.1

Reorder $x^{3}$ and $2$ .

$y^{4} + \frac{3 x^{4} y^{3}}{2} + \frac{2 \cdot x^{3} - 11 x^{3}}{4} + \frac{5 y^{4}}{2}$

Step 6.2

Subtract $11 x^{3}$ from $2 \cdot x^{3}$ .

$y^{4} + \frac{3 x^{4} y^{3}}{2} + \frac{- 9 \cdot x^{3}}{4} + \frac{5 y^{4}}{2}$

Step 7

Move the negative in front of the fraction.

$y^{4} + \frac{3 x^{4} y^{3}}{2} - \frac{9 x^{3}}{4} + \frac{5 y^{4}}{2}$

Step 8

To write $y^{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x^{4} y^{3}}{2} - \frac{9 x^{3}}{4} + y^{4} \cdot \frac{2}{2} + \frac{5 y^{4}}{2}$

Step 9

Simplify terms.

Tap for more steps...

Step 9.1

Combine $y^{4}$ and $\frac{2}{2}$ .

$\frac{3 x^{4} y^{3}}{2} - \frac{9 x^{3}}{4} + \frac{y^{4} \cdot 2}{2} + \frac{5 y^{4}}{2}$

Step 9.2

Combine the numerators over the common denominator.

$\frac{3 x^{4} y^{3}}{2} - \frac{9 x^{3}}{4} + \frac{y^{4} \cdot 2 + 5 y^{4}}{2}$

Step 9.3

Combine the numerators over the common denominator.

$\frac{3 x^{4} y^{3} + y^{4} \cdot 2 + 5 y^{4}}{2} + \frac{- 9 x^{3}}{4}$

Step 10

Move $2$ to the left of $y^{4}$ .

$\frac{3 x^{4} y^{3} + 2 y^{4} + 5 y^{4}}{2} + \frac{- 9 x^{3}}{4}$

Step 11

Add $2 y^{4}$ and $5 y^{4}$ .

$\frac{3 x^{4} y^{3} + 7 y^{4}}{2} + \frac{- 9 x^{3}}{4}$

Step 12

Simplify each term.

Tap for more steps...

Step 12.1

Factor $y^{3}$ out of $3 x^{4} y^{3} + 7 y^{4}$ .

Tap for more steps...

Step 12.1.1

Factor $y^{3}$ out of $3 x^{4} y^{3}$ .

$\frac{y^{3} (3 x^{4}) + 7 y^{4}}{2} + \frac{- 9 x^{3}}{4}$

Step 12.1.2

Factor $y^{3}$ out of $7 y^{4}$ .

$\frac{y^{3} (3 x^{4}) + y^{3} (7 y)}{2} + \frac{- 9 x^{3}}{4}$

Step 12.1.3

Factor $y^{3}$ out of $y^{3} (3 x^{4}) + y^{3} (7 y)$ .

$\frac{y^{3} (3 x^{4} + 7 y)}{2} + \frac{- 9 x^{3}}{4}$

Step 12.2

Move the negative in front of the fraction.

$\frac{y^{3} (3 x^{4} + 7 y)}{2} - \frac{9 x^{3}}{4}$

Step 13

To write $\frac{y^{3} (3 x^{4} + 7 y)}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y^{3} (3 x^{4} + 7 y)}{2} \cdot \frac{2}{2} - \frac{9 x^{3}}{4}$

Step 14

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 14.1

Multiply $\frac{y^{3} (3 x^{4} + 7 y)}{2}$ by $\frac{2}{2}$ .

$\frac{y^{3} (3 x^{4} + 7 y) \cdot 2}{2 \cdot 2} - \frac{9 x^{3}}{4}$

Step 14.2

Multiply $2$ by $2$ .

$\frac{y^{3} (3 x^{4} + 7 y) \cdot 2}{4} - \frac{9 x^{3}}{4}$

Step 15

Combine the numerators over the common denominator.

$\frac{y^{3} (3 x^{4} + 7 y) \cdot 2 - 9 x^{3}}{4}$

Step 16

Simplify the numerator.

Tap for more steps...

Step 16.1

Apply the distributive property.

$\frac{(y^{3} (3 x^{4}) + y^{3} (7 y)) \cdot 2 - 9 x^{3}}{4}$

Step 16.2

Rewrite using the commutative property of multiplication.

$\frac{(3 y^{3} x^{4} + y^{3} (7 y)) \cdot 2 - 9 x^{3}}{4}$

Step 16.3

Rewrite using the commutative property of multiplication.

$\frac{(3 y^{3} x^{4} + 7 y^{3} y) \cdot 2 - 9 x^{3}}{4}$

Step 16.4

Multiply $y^{3}$ by $y$ by adding the exponents.

Tap for more steps...

Step 16.4.1

Move $y$ .

$\frac{(3 y^{3} x^{4} + 7 (y \cdot y^{3})) \cdot 2 - 9 x^{3}}{4}$

Step 16.4.2

Multiply $y$ by $y^{3}$ .

Tap for more steps...

Step 16.4.2.1

Raise $y$ to the power of $1$ .

$\frac{(3 y^{3} x^{4} + 7 (y^{1} y^{3})) \cdot 2 - 9 x^{3}}{4}$

Step 16.4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(3 y^{3} x^{4} + 7 y^{1 + 3}) \cdot 2 - 9 x^{3}}{4}$

Step 16.4.3

Add $1$ and $3$ .

$\frac{(3 y^{3} x^{4} + 7 y^{4}) \cdot 2 - 9 x^{3}}{4}$

Step 16.5

Apply the distributive property.

$\frac{3 y^{3} x^{4} \cdot 2 + 7 y^{4} \cdot 2 - 9 x^{3}}{4}$

Step 16.6

Multiply $2$ by $3$ .

$\frac{6 y^{3} x^{4} + 7 y^{4} \cdot 2 - 9 x^{3}}{4}$

Step 16.7

Multiply $2$ by $7$ .

$\frac{6 y^{3} x^{4} + 14 y^{4} - 9 x^{3}}{4}$