Basic Math Examples

$z^{2} - (8 (7 z^{2} - 5 z + 9)) - (5 z^{2} - 8 z - 3)$

Step 1

Apply the distributive property.

$z^{2} - (8 (7 z^{2}) + 8 (- 5 z) + 8 \cdot 9) - (5 z^{2} - 8 z - 3)$

Step 2

Simplify.

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Step 2.1

Multiply $7$ by $8$ .

$z^{2} - (56 z^{2} + 8 (- 5 z) + 8 \cdot 9) - (5 z^{2} - 8 z - 3)$

Step 2.2

Multiply $- 5$ by $8$ .

$z^{2} - (56 z^{2} - 40 z + 8 \cdot 9) - (5 z^{2} - 8 z - 3)$

Step 2.3

Multiply $8$ by $9$ .

$z^{2} - (56 z^{2} - 40 z + 72) - (5 z^{2} - 8 z - 3)$

Step 3

Apply the distributive property.

$z^{2} - (56 z^{2}) - (- 40 z) - 1 \cdot 72 - (5 z^{2} - 8 z - 3)$

Step 4

Simplify.

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Step 4.1

Multiply $56$ by $- 1$ .

$z^{2} - 56 z^{2} - (- 40 z) - 1 \cdot 72 - (5 z^{2} - 8 z - 3)$

Step 4.2

Multiply $- 40$ by $- 1$ .

$z^{2} - 56 z^{2} + 40 z - 1 \cdot 72 - (5 z^{2} - 8 z - 3)$

Step 4.3

Multiply $- 1$ by $72$ .

$z^{2} - 56 z^{2} + 40 z - 72 - (5 z^{2} - 8 z - 3)$

Step 5

Apply the distributive property.

$z^{2} - 56 z^{2} + 40 z - 72 - (5 z^{2}) - (- 8 z) - - 3$

Step 6

Simplify.

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Step 6.1

Multiply $5$ by $- 1$ .

$z^{2} - 56 z^{2} + 40 z - 72 - 5 z^{2} - (- 8 z) - - 3$

Step 6.2

Multiply $- 8$ by $- 1$ .

$z^{2} - 56 z^{2} + 40 z - 72 - 5 z^{2} + 8 z - - 3$

Step 6.3

Multiply $- 1$ by $- 3$ .

$z^{2} - 56 z^{2} + 40 z - 72 - 5 z^{2} + 8 z + 3$

Step 7

Subtract $56 z^{2}$ from $z^{2}$ .

$- 55 z^{2} + 40 z - 72 - 5 z^{2} + 8 z + 3$

Step 8

Subtract $5 z^{2}$ from $- 55 z^{2}$ .

$- 60 z^{2} + 40 z - 72 + 8 z + 3$

Step 9

Add $40 z$ and $8 z$ .

$- 60 z^{2} + 48 z - 72 + 3$

Step 10

Add $- 72$ and $3$ .

$- 60 z^{2} + 48 z - 69$

Step 11

Factor $- 3$ out of $- 60 z^{2} + 48 z - 69$ .

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Step 11.1

Factor $- 3$ out of $- 60 z^{2}$ .

$- 3 (20 z^{2}) + 48 z - 69$

Step 11.2

Factor $- 3$ out of $48 z$ .

$- 3 (20 z^{2}) - 3 (- 16 z) - 69$

Step 11.3

Factor $- 3$ out of $- 69$ .

$- 3 (20 z^{2}) - 3 (- 16 z) - 3 (23)$

Step 11.4

Factor $- 3$ out of $- 3 (20 z^{2}) - 3 (- 16 z)$ .

$- 3 (20 z^{2} - 16 z) - 3 (23)$

Step 11.5

Factor $- 3$ out of $- 3 (20 z^{2} - 16 z) - 3 (23)$ .

$- 3 (20 z^{2} - 16 z + 23)$