Algebra Examples

$3 x (x y - 4) + 3 (4 x y + 3) - x y (x^{2} y - 1)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.2.1

Move $x$ .

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

Step 1.2.2

Multiply $x$ by $x$ .

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

Step 1.3

Multiply $- 4$ by $3$ .

$3 x^{2} y - 12 x + 3 (4 x y + 3) - x y (x^{2} y - 1)$

Step 1.4

Apply the distributive property.

$3 x^{2} y - 12 x + 3 (4 x y) + 3 \cdot 3 - x y (x^{2} y - 1)$

Step 1.5

Multiply $4$ by $3$ .

$3 x^{2} y - 12 x + 12 (x y) + 3 \cdot 3 - x y (x^{2} y - 1)$

Step 1.6

Multiply $3$ by $3$ .

$3 x^{2} y - 12 x + 12 (x y) + 9 - x y (x^{2} y - 1)$

Step 1.7

Apply the distributive property.

$3 x^{2} y - 12 x + 12 x y + 9 - x y (x^{2} y) - x y \cdot - 1$

Step 1.8

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

Tap for more steps...

Step 1.8.1

Move $x^{2}$ .

$3 x^{2} y - 12 x + 12 x y + 9 - (x^{2} x) y \cdot y - x y \cdot - 1$

Step 1.8.2

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

Tap for more steps...

Step 1.8.2.1

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

$3 x^{2} y - 12 x + 12 x y + 9 - (x^{2} x^{1}) y \cdot y - x y \cdot - 1$

Step 1.8.2.2

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

$3 x^{2} y - 12 x + 12 x y + 9 - x^{2 + 1} y \cdot y - x y \cdot - 1$

Step 1.8.3

Add $2$ and $1$ .

$3 x^{2} y - 12 x + 12 x y + 9 - x^{3} y \cdot y - x y \cdot - 1$

Step 1.9

Multiply $- x y \cdot - 1$ .

Tap for more steps...

Step 1.9.1

Multiply $- 1$ by $- 1$ .

$3 x^{2} y - 12 x + 12 x y + 9 - x^{3} y \cdot y + 1 x y$

Step 1.9.2

Multiply $x$ by $1$ .

$3 x^{2} y - 12 x + 12 x y + 9 - x^{3} y \cdot y + x y$

Step 1.10

Multiply $y$ by $y$ by adding the exponents.

Tap for more steps...

Step 1.10.1

Move $y$ .

$3 x^{2} y - 12 x + 12 x y + 9 - x^{3} (y \cdot y) + x y$

Step 1.10.2

Multiply $y$ by $y$ .

$3 x^{2} y - 12 x + 12 x y + 9 - x^{3} y^{2} + x y$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Add $12 x y$ and $x y$ .

$3 x^{2} y - 12 x + 13 x y + 9 - x^{3} y^{2}$

Step 2.2

Simplify the expression.

Tap for more steps...

Step 2.2.1

Move $9$ .

$3 x^{2} y - 12 x + 13 x y - x^{3} y^{2} + 9$

Step 2.2.2

Move $- 12 x$ .

$3 x^{2} y + 13 x y - x^{3} y^{2} - 12 x + 9$

Step 2.2.3

Move $13 x y$ .

$3 x^{2} y - x^{3} y^{2} + 13 x y - 12 x + 9$

Step 2.2.4

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

$- x^{3} y^{2} + 3 x^{2} y + 13 x y - 12 x + 9$