Precalculus Examples

$25 - {(z + 5)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(z + 5)}^{2}$ as $(z + 5) (z + 5)$ .

$25 - ((z + 5) (z + 5))$

Step 1.2

Expand $(z + 5) (z + 5)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$25 - (z (z + 5) + 5 (z + 5))$

Step 1.2.2

Apply the distributive property.

$25 - (z \cdot z + z \cdot 5 + 5 (z + 5))$

Step 1.2.3

Apply the distributive property.

$25 - (z \cdot z + z \cdot 5 + 5 z + 5 \cdot 5)$

$25 - (z \cdot z + z \cdot 5 + 5 z + 5 \cdot 5)$

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 $z$ .

$25 - (z^{2} + z \cdot 5 + 5 z + 5 \cdot 5)$

Step 1.3.1.2

Move $5$ to the left of $z$ .

$25 - (z^{2} + 5 \cdot z + 5 z + 5 \cdot 5)$

Step 1.3.1.3

Multiply $5$ by $5$ .

$25 - (z^{2} + 5 z + 5 z + 25)$

$25 - (z^{2} + 5 z + 5 z + 25)$

Step 1.3.2

Add $5 z$ and $5 z$ .

$25 - (z^{2} + 10 z + 25)$

$25 - (z^{2} + 10 z + 25)$

Step 1.4

Apply the distributive property.

$25 - z^{2} - (10 z) - 1 \cdot 25$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $10$ by $- 1$ .

$25 - z^{2} - 10 z - 1 \cdot 25$

Step 1.5.2

Multiply $- 1$ by $25$ .

$25 - z^{2} - 10 z - 25$

$25 - z^{2} - 10 z - 25$

$25 - z^{2} - 10 z - 25$

Step 2

Combine the opposite terms in $25 - z^{2} - 10 z - 25$ .

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Step 2.1

Subtract $25$ from $25$ .

$- z^{2} - 10 z + 0$

Step 2.2

Add $- z^{2} - 10 z$ and $0$ .

$- z^{2} - 10 z$

$- z^{2} - 10 z$

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