Finite Math Examples

$(x - x y + 3 y) (x - 2 y)$

Step 1

Expand $(x - x y + 3 y) (x - 2 y)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x + x (- 2 y) - x y x - x y (- 2 y) + 3 y x + 3 y (- 2 y)$

Step 2

Simplify each term.

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Step 2.1

Multiply $x$ by $x$ .

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

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 2.3

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

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Step 2.3.1

Move $x$ .

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

Step 2.3.2

Multiply $x$ by $x$ .

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

Step 2.4

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

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Step 2.4.1

Move $y$ .

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

Step 2.4.2

Multiply $y$ by $y$ .

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

Step 2.5

Multiply $- 2$ by $- 1$ .

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

Step 2.6

Rewrite using the commutative property of multiplication.

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

Step 2.7

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

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Step 2.7.1

Move $y$ .

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

Step 2.7.2

Multiply $y$ by $y$ .

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

Step 2.8

Multiply $3$ by $- 2$ .

$x^{2} - 2 x y - x^{2} y + 2 x y^{2} + 3 y x - 6 y^{2}$

Step 3

Add $- 2 x y$ and $3 y x$ .

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Step 3.1

Move $y$ .

$x^{2} - 2 x y + 3 x y - x^{2} y + 2 x y^{2} - 6 y^{2}$

Step 3.2

Add $- 2 x y$ and $3 x y$ .

$x^{2} + 1 x y - x^{2} y + 2 x y^{2} - 6 y^{2}$

Step 4

Multiply $x$ by $1$ .

$x^{2} + x y - x^{2} y + 2 x y^{2} - 6 y^{2}$

Step 5

Move $x y$ .

$x^{2} - x^{2} y + 2 x y^{2} + x y - 6 y^{2}$

Step 6

Move $x^{2}$ .

$- x^{2} y + 2 x y^{2} + x^{2} + x y - 6 y^{2}$