Basic Math Examples

$(r - 3) (2 r^{2} - 5)$

Step 1

Expand $(r - 3) (2 r^{2} - 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$r (2 r^{2} - 5) - 3 (2 r^{2} - 5)$

Step 1.2

Apply the distributive property.

$r (2 r^{2}) + r \cdot - 5 - 3 (2 r^{2} - 5)$

Step 1.3

Apply the distributive property.

$r (2 r^{2}) + r \cdot - 5 - 3 (2 r^{2}) - 3 \cdot - 5$

Step 2

Simplify 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.

$2 r \cdot r^{2} + r \cdot - 5 - 3 (2 r^{2}) - 3 \cdot - 5$

Step 2.1.2

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

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Step 2.1.2.1

Move $r^{2}$ .

$2 (r^{2} r) + r \cdot - 5 - 3 (2 r^{2}) - 3 \cdot - 5$

Step 2.1.2.2

Multiply $r^{2}$ by $r$ .

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Step 2.1.2.2.1

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

$2 (r^{2} r^{1}) + r \cdot - 5 - 3 (2 r^{2}) - 3 \cdot - 5$

Step 2.1.2.2.2

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

$2 r^{2 + 1} + r \cdot - 5 - 3 (2 r^{2}) - 3 \cdot - 5$

Step 2.1.2.3

Add $2$ and $1$ .

$2 r^{3} + r \cdot - 5 - 3 (2 r^{2}) - 3 \cdot - 5$

Step 2.1.3

Move $- 5$ to the left of $r$ .

$2 r^{3} - 5 \cdot r - 3 (2 r^{2}) - 3 \cdot - 5$

Step 2.1.4

Multiply $2$ by $- 3$ .

$2 r^{3} - 5 r - 6 r^{2} - 3 \cdot - 5$

Step 2.1.5

Multiply $- 3$ by $- 5$ .

$2 r^{3} - 5 r - 6 r^{2} + 15$

Step 2.2

Move $- 5 r$ .

$2 r^{3} - 6 r^{2} - 5 r + 15$