Precalculus Examples

$(2 r^{2} - 5) (2 r^{2} + 5)$

Step 1

Expand $(2 r^{2} - 5) (2 r^{2} + 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 r^{2} (2 r^{2} + 5) - 5 (2 r^{2} + 5)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

Multiply $r^{2}$ by $r^{2}$ by adding the exponents.

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Step 2.1.2.1

Move $r^{2}$ .

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

Step 2.1.2.2

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

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

Step 2.1.2.3

Add $2$ and $2$ .

$2 \cdot 2 r^{4} + 2 r^{2} \cdot 5 - 5 (2 r^{2}) - 5 \cdot 5$

Step 2.1.3

Multiply $2$ by $2$ .

$4 r^{4} + 2 r^{2} \cdot 5 - 5 (2 r^{2}) - 5 \cdot 5$

Step 2.1.4

Multiply $5$ by $2$ .

$4 r^{4} + 10 r^{2} - 5 (2 r^{2}) - 5 \cdot 5$

Step 2.1.5

Multiply $2$ by $- 5$ .

$4 r^{4} + 10 r^{2} - 10 r^{2} - 5 \cdot 5$

Step 2.1.6

Multiply $- 5$ by $5$ .

$4 r^{4} + 10 r^{2} - 10 r^{2} - 25$

Step 2.2

Subtract $10 r^{2}$ from $10 r^{2}$ .

$4 r^{4} + 0 - 25$

Step 2.3

Add $4 r^{4}$ and $0$ .

$4 r^{4} - 25$