Algebra Examples

$(z^{2} + 3 z) - (3 z^{2} + 7 z + 16) - (4 z - 13)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$z^{2} + 3 z - (3 z^{2}) - (7 z) - 1 \cdot 16 - (4 z - 13)$

Step 1.2

Simplify.

Tap for more steps...

Step 1.2.1

Multiply $3$ by $- 1$ .

$z^{2} + 3 z - 3 z^{2} - (7 z) - 1 \cdot 16 - (4 z - 13)$

Step 1.2.2

Multiply $7$ by $- 1$ .

$z^{2} + 3 z - 3 z^{2} - 7 z - 1 \cdot 16 - (4 z - 13)$

Step 1.2.3

Multiply $- 1$ by $16$ .

$z^{2} + 3 z - 3 z^{2} - 7 z - 16 - (4 z - 13)$

Step 1.3

Apply the distributive property.

$z^{2} + 3 z - 3 z^{2} - 7 z - 16 - (4 z) - - 13$

Step 1.4

Multiply $4$ by $- 1$ .

$z^{2} + 3 z - 3 z^{2} - 7 z - 16 - 4 z - - 13$

Step 1.5

Multiply $- 1$ by $- 13$ .

$z^{2} + 3 z - 3 z^{2} - 7 z - 16 - 4 z + 13$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Subtract $3 z^{2}$ from $z^{2}$ .

$- 2 z^{2} + 3 z - 7 z - 16 - 4 z + 13$

Step 2.2

Subtract $7 z$ from $3 z$ .

$- 2 z^{2} - 4 z - 16 - 4 z + 13$

Step 2.3

Subtract $4 z$ from $- 4 z$ .

$- 2 z^{2} - 8 z - 16 + 13$

Step 2.4

Add $- 16$ and $13$ .

$- 2 z^{2} - 8 z - 3$