Basic Math Examples

${(z - 3 y)}^{2}$

Step 1

Rewrite ${(z - 3 y)}^{2}$ as $(z - 3 y) (z - 3 y)$ .

$(z - 3 y) (z - 3 y)$

Step 2

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

Tap for more steps...

Step 2.1

Apply the distributive property.

$z (z - 3 y) - 3 y (z - 3 y)$

Step 2.2

Apply the distributive property.

$z \cdot z + z (- 3 y) - 3 y (z - 3 y)$

Step 2.3

Apply the distributive property.

$z \cdot z + z (- 3 y) - 3 y z - 3 y (- 3 y)$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $z$ by $z$ .

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

Step 3.1.2

Rewrite using the commutative property of multiplication.

$z^{2} - 3 z y - 3 y z - 3 y (- 3 y)$

Step 3.1.3

Rewrite using the commutative property of multiplication.

$z^{2} - 3 z y - 3 y z - 3 \cdot - 3 y \cdot y$

Step 3.1.4

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

Tap for more steps...

Step 3.1.4.1

Move $y$ .

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

Step 3.1.4.2

Multiply $y$ by $y$ .

$z^{2} - 3 z y - 3 y z - 3 \cdot - 3 y^{2}$

Step 3.1.5

Multiply $- 3$ by $- 3$ .

$z^{2} - 3 z y - 3 y z + 9 y^{2}$

Step 3.2

Subtract $3 y z$ from $- 3 z y$ .

Tap for more steps...

Step 3.2.1

Move $z$ .

$z^{2} - 3 y z - 3 y z + 9 y^{2}$

Step 3.2.2

Subtract $3 y z$ from $- 3 y z$ .

$z^{2} - 6 y z + 9 y^{2}$

Step 4

Move $z^{2}$ .

$- 6 y z + 9 y^{2} + z^{2}$

Step 5

Reorder $- 6 y z$ and $9 y^{2}$ .

$9 y^{2} - 6 y z + z^{2}$