Basic Math Examples

${(z - 1)}^{2} - 16$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(z - 1)}^{2}$ as $(z - 1) (z - 1)$ .

$(z - 1) (z - 1) - 16$

Step 1.2

Expand $(z - 1) (z - 1)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$z (z - 1) - 1 (z - 1) - 16$

Step 1.2.2

Apply the distributive property.

$z \cdot z + z \cdot - 1 - 1 (z - 1) - 16$

Step 1.2.3

Apply the distributive property.

$z \cdot z + z \cdot - 1 - 1 z - 1 \cdot - 1 - 16$

$z \cdot z + z \cdot - 1 - 1 z - 1 \cdot - 1 - 16$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $z$ by $z$ .

$z^{2} + z \cdot - 1 - 1 z - 1 \cdot - 1 - 16$

Step 1.3.1.2

Move $- 1$ to the left of $z$ .

$z^{2} - 1 \cdot z - 1 z - 1 \cdot - 1 - 16$

Step 1.3.1.3

Rewrite $- 1 z$ as $- z$ .

$z^{2} - z - 1 z - 1 \cdot - 1 - 16$

Step 1.3.1.4

Rewrite $- 1 z$ as $- z$ .

$z^{2} - z - z - 1 \cdot - 1 - 16$

Step 1.3.1.5

Multiply $- 1$ by $- 1$ .

$z^{2} - z - z + 1 - 16$

$z^{2} - z - z + 1 - 16$

Step 1.3.2

Subtract $z$ from $- z$ .

$z^{2} - 2 z + 1 - 16$

$z^{2} - 2 z + 1 - 16$

$z^{2} - 2 z + 1 - 16$

Step 2

Subtract $16$ from $1$ .

$z^{2} - 2 z - 15$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$