Algebra Examples

$(3 x y - 2 y) (3 x y - 8 y z)$

Step 1

Expand $(3 x y - 2 y) (3 x y - 8 y z)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 x y (3 x y - 8 y z) - 2 y (3 x y - 8 y z)$

Step 1.2

Apply the distributive property.

$3 x y (3 x y) + 3 x y (- 8 y z) - 2 y (3 x y - 8 y z)$

Step 1.3

Apply the distributive property.

$3 x y (3 x y) + 3 x y (- 8 y z) - 2 y (3 x y) - 2 y (- 8 y z)$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $x$ .

$3 (x \cdot x) y (3 y) + 3 x y (- 8 y z) - 2 y (3 x y) - 2 y (- 8 y z)$

Step 2.1.2

Multiply $x$ by $x$ .

$3 x^{2} y (3 y) + 3 x y (- 8 y z) - 2 y (3 x y) - 2 y (- 8 y z)$

Step 2.2

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

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Step 2.2.1

Move $y$ .

$3 x^{2} (y \cdot y) \cdot 3 + 3 x y (- 8 y z) - 2 y (3 x y) - 2 y (- 8 y z)$

Step 2.2.2

Multiply $y$ by $y$ .

$3 x^{2} y^{2} \cdot 3 + 3 x y (- 8 y z) - 2 y (3 x y) - 2 y (- 8 y z)$

Step 2.3

Multiply $3$ by $3$ .

$9 x^{2} y^{2} + 3 x y (- 8 y z) - 2 y (3 x y) - 2 y (- 8 y z)$

Step 2.4

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

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Step 2.4.1

Move $y$ .

$9 x^{2} y^{2} + 3 x (y \cdot y) (- 8 z) - 2 y (3 x y) - 2 y (- 8 y z)$

Step 2.4.2

Multiply $y$ by $y$ .

$9 x^{2} y^{2} + 3 x y^{2} (- 8 z) - 2 y (3 x y) - 2 y (- 8 y z)$

Step 2.5

Multiply $- 8$ by $3$ .

$9 x^{2} y^{2} - 24 x y^{2} z - 2 y (3 x y) - 2 y (- 8 y z)$

Step 2.6

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

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Step 2.6.1

Move $y$ .

$9 x^{2} y^{2} - 24 x y^{2} z - 2 (y \cdot y) (3 x) - 2 y (- 8 y z)$

Step 2.6.2

Multiply $y$ by $y$ .

$9 x^{2} y^{2} - 24 x y^{2} z - 2 y^{2} (3 x) - 2 y (- 8 y z)$

Step 2.7

Rewrite using the commutative property of multiplication.

$9 x^{2} y^{2} - 24 x y^{2} z - 2 \cdot 3 y^{2} x - 2 y (- 8 y z)$

Step 2.8

Multiply $- 2$ by $3$ .

$9 x^{2} y^{2} - 24 x y^{2} z - 6 y^{2} x - 2 y (- 8 y z)$

Step 2.9

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

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Step 2.9.1

Move $y$ .

$9 x^{2} y^{2} - 24 x y^{2} z - 6 y^{2} x - 2 (y \cdot y) (- 8 z)$

Step 2.9.2

Multiply $y$ by $y$ .

$9 x^{2} y^{2} - 24 x y^{2} z - 6 y^{2} x - 2 y^{2} (- 8 z)$

Step 2.10

Rewrite using the commutative property of multiplication.

$9 x^{2} y^{2} - 24 x y^{2} z - 6 y^{2} x - 2 \cdot - 8 y^{2} z$

Step 2.11

Multiply $- 2$ by $- 8$ .

$9 x^{2} y^{2} - 24 x y^{2} z - 6 y^{2} x + 16 y^{2} z$