Pre-Algebra Examples

$(3 x + 2 y - 1) (- x y)$

Step 1

Apply the distributive property.

$3 x (- x y) + 2 y (- x y) - 1 (- x y)$

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $x$ .

$3 (x \cdot x) (- 1 y) + 2 y (- x y) - 1 (- x y)$

Step 2.1.2

Multiply $x$ by $x$ .

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

Step 2.2

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

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Step 2.2.1

Move $y$ .

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

Step 2.2.2

Multiply $y$ by $y$ .

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

Step 2.3

Multiply $- 1 (- x y)$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

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

Step 2.3.2

Multiply $x$ by $1$ .

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

Step 3

Simplify each term.

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Step 3.1

Rewrite using the commutative property of multiplication.

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

Step 3.2

Multiply $3$ by $- 1$ .

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

Step 3.3

Rewrite using the commutative property of multiplication.

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

Step 3.4

Multiply $2$ by $- 1$ .

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