Basic Math Examples

$2 (2 r + 5) (r - 2)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$(2 (2 r) + 2 \cdot 5) (r - 2)$

Step 1.2

Multiply.

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Step 1.2.1

Multiply $2$ by $2$ .

$(4 r + 2 \cdot 5) (r - 2)$

Step 1.2.2

Multiply $2$ by $5$ .

$(4 r + 10) (r - 2)$

Step 2

Expand $(4 r + 10) (r - 2)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$4 r (r - 2) + 10 (r - 2)$

Step 2.2

Apply the distributive property.

$4 r \cdot r + 4 r \cdot - 2 + 10 (r - 2)$

Step 2.3

Apply the distributive property.

$4 r \cdot r + 4 r \cdot - 2 + 10 r + 10 \cdot - 2$

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

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Step 3.1.1.1

Move $r$ .

$4 (r \cdot r) + 4 r \cdot - 2 + 10 r + 10 \cdot - 2$

Step 3.1.1.2

Multiply $r$ by $r$ .

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

Step 3.1.2

Multiply $- 2$ by $4$ .

$4 r^{2} - 8 r + 10 r + 10 \cdot - 2$

Step 3.1.3

Multiply $10$ by $- 2$ .

$4 r^{2} - 8 r + 10 r - 20$

Step 3.2

Add $- 8 r$ and $10 r$ .

$4 r^{2} + 2 r - 20$