Basic Math Examples

${(z - e)}^{2}$

Step 1

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

$(z - e) (z - e)$

Step 2

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

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Step 2.1

Apply the distributive property.

$z (z - e) - e (z - e)$

Step 2.2

Apply the distributive property.

$z \cdot z + z (- e) - e (z - e)$

Step 2.3

Apply the distributive property.

$z \cdot z + z (- e) - e z - e (- e)$

$z \cdot z + z (- e) - e z - e (- e)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $z$ by $z$ .

$z^{2} + z (- e) - e z - e (- e)$

Step 3.1.2

Multiply $- e (- e)$ .

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Step 3.1.2.1

Multiply $- 1$ by $- 1$ .

$z^{2} + z (- e) - e z + 1 e e$

Step 3.1.2.2

Multiply $e$ by $1$ .

$z^{2} + z (- e) - e z + e e$

Step 3.1.2.3

Raise $e$ to the power of $1$ .

$z^{2} + z (- e) - e z + e^{1} e$

Step 3.1.2.4

Raise $e$ to the power of $1$ .

$z^{2} + z (- e) - e z + e^{1} e^{1}$

Step 3.1.2.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$z^{2} + z (- e) - e z + e^{1 + 1}$

Step 3.1.2.6

Add $1$ and $1$ .

$z^{2} + z (- e) - e z + e^{2}$

$z^{2} + z (- e) - e z + e^{2}$

$z^{2} + z (- e) - e z + e^{2}$

Step 3.2

Move $e$ .

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

Step 3.3

Subtract $z e$ from $- 1 \cdot z e$ .

$z^{2} - 2 z e + e^{2}$

$z^{2} - 2 z e + e^{2}$

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