Finite Math Examples

$(x^{2} y + x^{2}) d x + (y^{2} x - y^{2}) d y + 0$

Step 1

Add $(x^{2} y + x^{2}) d x + (y^{2} x - y^{2}) d y$ and $0$ .

$(x^{2} y + x^{2}) d x + (y^{2} x - y^{2}) d y$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the distributive property.

$(x^{2} y d + x^{2} d) x + (y^{2} x - y^{2}) d y$

Step 2.2

Apply the distributive property.

$x^{2} y d x + x^{2} d x + (y^{2} x - y^{2}) d y$

Step 2.3

Multiply $x^{2}$ by $x$ by adding the exponents.

Tap for more steps...

Step 2.3.1

Move $x$ .

$x \cdot x^{2} y d + x^{2} d x + (y^{2} x - y^{2}) d y$

Step 2.3.2

Multiply $x$ by $x^{2}$ .

Tap for more steps...

Step 2.3.2.1

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

$x^{1} x^{2} y d + x^{2} d x + (y^{2} x - y^{2}) d y$

Step 2.3.2.2

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

$x^{1 + 2} y d + x^{2} d x + (y^{2} x - y^{2}) d y$

Step 2.3.3

Add $1$ and $2$ .

$x^{3} y d + x^{2} d x + (y^{2} x - y^{2}) d y$

Step 2.4

Multiply $x^{2}$ by $x$ by adding the exponents.

Tap for more steps...

Step 2.4.1

Move $x$ .

$x^{3} y d + x \cdot x^{2} d + (y^{2} x - y^{2}) d y$

Step 2.4.2

Multiply $x$ by $x^{2}$ .

Tap for more steps...

Step 2.4.2.1

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

$x^{3} y d + x^{1} x^{2} d + (y^{2} x - y^{2}) d y$

Step 2.4.2.2

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

$x^{3} y d + x^{1 + 2} d + (y^{2} x - y^{2}) d y$

Step 2.4.3

Add $1$ and $2$ .

$x^{3} y d + x^{3} d + (y^{2} x - y^{2}) d y$

Step 2.5

Apply the distributive property.

$x^{3} y d + x^{3} d + (y^{2} x d - y^{2} d) y$

Step 2.6

Apply the distributive property.

$x^{3} y d + x^{3} d + y^{2} x d y - y^{2} d y$

Step 2.7

Multiply $y^{2}$ by $y$ by adding the exponents.

Tap for more steps...

Step 2.7.1

Move $y$ .

$x^{3} y d + x^{3} d + y \cdot y^{2} x d - y^{2} d y$

Step 2.7.2

Multiply $y$ by $y^{2}$ .

Tap for more steps...

Step 2.7.2.1

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

$x^{3} y d + x^{3} d + y^{1} y^{2} x d - y^{2} d y$

Step 2.7.2.2

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

$x^{3} y d + x^{3} d + y^{1 + 2} x d - y^{2} d y$

Step 2.7.3

Add $1$ and $2$ .

$x^{3} y d + x^{3} d + y^{3} x d - y^{2} d y$

Step 2.8

Multiply $y^{2}$ by $y$ by adding the exponents.

Tap for more steps...

Step 2.8.1

Move $y$ .

$x^{3} y d + x^{3} d + y^{3} x d - (y \cdot y^{2}) d$

Step 2.8.2

Multiply $y$ by $y^{2}$ .

Tap for more steps...

Step 2.8.2.1

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

$x^{3} y d + x^{3} d + y^{3} x d - (y^{1} y^{2}) d$

Step 2.8.2.2

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

$x^{3} y d + x^{3} d + y^{3} x d - y^{1 + 2} d$

Step 2.8.3

Add $1$ and $2$ .

$x^{3} y d + x^{3} d + y^{3} x d - y^{3} d$