Basic Math Examples

$(r - 0) \cdot (r - 5) \cdot (r + 1)$

Step 1

Simplify by multiplying through.

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Step 1.1

Subtract $0$ from $r$ .

$r \cdot (r - 5) \cdot (r + 1)$

Step 1.2

Apply the distributive property.

$(r \cdot r + r \cdot - 5) \cdot (r + 1)$

Step 1.3

Simplify the expression.

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Step 1.3.1

Multiply $r$ by $r$ .

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

Step 1.3.2

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

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

Step 2

Expand $(r^{2} - 5 r) (r + 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

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

Step 3.1.1.1.2

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

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

Step 3.1.1.2

Add $2$ and $1$ .

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

Step 3.1.2

Multiply $r^{2}$ by $1$ .

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

Step 3.1.3

Multiply $r$ by $r$ by adding the exponents.

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Step 3.1.3.1

Move $r$ .

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

Step 3.1.3.2

Multiply $r$ by $r$ .

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

Step 3.1.4

Multiply $- 5$ by $1$ .

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

Step 3.2

Subtract $5 r^{2}$ from $r^{2}$ .

$r^{3} - 4 r^{2} - 5 r$