Finite Math Examples

$- 3 {(p + h)}^{2} - 7 (p + h) + 500$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(p + h)}^{2}$ as $(p + h) (p + h)$ .

$- 3 ((p + h) (p + h)) - 7 (p + h) + 500$

Step 1.2

Expand $(p + h) (p + h)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$- 3 (p (p + h) + h (p + h)) - 7 (p + h) + 500$

Step 1.2.2

Apply the distributive property.

$- 3 (p \cdot p + p h + h (p + h)) - 7 (p + h) + 500$

Step 1.2.3

Apply the distributive property.

$- 3 (p \cdot p + p h + h p + h \cdot h) - 7 (p + h) + 500$

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 $p$ by $p$ .

$- 3 (p^{2} + p h + h p + h \cdot h) - 7 (p + h) + 500$

Step 1.3.1.2

Multiply $h$ by $h$ .

$- 3 (p^{2} + p h + h p + h^{2}) - 7 (p + h) + 500$

Step 1.3.2

Add $p h$ and $h p$ .

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Step 1.3.2.1

Reorder $p$ and $h$ .

$- 3 (p^{2} + h p + h p + h^{2}) - 7 (p + h) + 500$

Step 1.3.2.2

Add $h p$ and $h p$ .

$- 3 (p^{2} + 2 h p + h^{2}) - 7 (p + h) + 500$

Step 1.4

Apply the distributive property.

$- 3 p^{2} - 3 (2 h p) - 3 h^{2} - 7 (p + h) + 500$

Step 1.5

Multiply $2$ by $- 3$ .

$- 3 p^{2} - 6 (h p) - 3 h^{2} - 7 (p + h) + 500$

Step 1.6

Apply the distributive property.

$- 3 p^{2} - 6 h p - 3 h^{2} - 7 p - 7 h + 500$

Step 2

Simplify the expression.

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Step 2.1

Move $- 7 p$ .

$- 3 p^{2} - 6 h p - 3 h^{2} - 7 h - 7 p + 500$

Step 2.2

Move $- 3 p^{2}$ .

$- 6 h p - 3 h^{2} - 3 p^{2} - 7 h - 7 p + 500$

Step 2.3

Reorder $- 6 h p$ and $- 3 h^{2}$ .

$- 3 h^{2} - 6 h p - 3 p^{2} - 7 h - 7 p + 500$