Basic Math Examples

$(- 5 + 9 p) (5 + 9 p)$

Step 1

Expand $(- 5 + 9 p) (5 + 9 p)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$- 5 (5 + 9 p) + 9 p (5 + 9 p)$

Step 1.2

Apply the distributive property.

$- 5 \cdot 5 - 5 (9 p) + 9 p (5 + 9 p)$

Step 1.3

Apply the distributive property.

$- 5 \cdot 5 - 5 (9 p) + 9 p \cdot 5 + 9 p (9 p)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $- 5 \cdot 5 - 5 (9 p) + 9 p \cdot 5 + 9 p (9 p)$ .

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Step 2.1.1

Reorder the factors in the terms $- 5 (9 p)$ and $9 p \cdot 5$ .

$- 5 \cdot 5 - 5 \cdot 9 p + 5 \cdot 9 p + 9 p (9 p)$

Step 2.1.2

Add $- 5 \cdot 9 p$ and $5 \cdot 9 p$ .

$- 5 \cdot 5 + 0 + 9 p (9 p)$

Step 2.1.3

Add $- 5 \cdot 5$ and $0$ .

$- 5 \cdot 5 + 9 p (9 p)$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $- 5$ by $5$ .

$- 25 + 9 p (9 p)$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$- 25 + 9 \cdot 9 p \cdot p$

Step 2.2.3

Multiply $p$ by $p$ by adding the exponents.

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Step 2.2.3.1

Move $p$ .

$- 25 + 9 \cdot 9 (p \cdot p)$

Step 2.2.3.2

Multiply $p$ by $p$ .

$- 25 + 9 \cdot 9 p^{2}$

Step 2.2.4

Multiply $9$ by $9$ .

$- 25 + 81 p^{2}$