Basic Math Examples

(r + 5) (r - 3)

$(r + 5) (r - 3)$

Step 1

Expand

(r + 5) (r - 3)

$(r + 5) (r - 3)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

r (r - 3) + 5 (r - 3)

$r (r - 3) + 5 (r - 3)$

Step 1.2

Apply the distributive property.

r \cdot r + r \cdot - 3 + 5 (r - 3)

$r \cdot r + r \cdot - 3 + 5 (r - 3)$

Step 1.3

Apply the distributive property.

r \cdot r + r \cdot - 3 + 5 r + 5 \cdot - 3

$r \cdot r + r \cdot - 3 + 5 r + 5 \cdot - 3$

r \cdot r + r \cdot - 3 + 5 r + 5 \cdot - 3

$r \cdot r + r \cdot - 3 + 5 r + 5 \cdot - 3$

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

Multiply

r

$r$ by

r

$r$ .

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

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

Step 2.1.2

Move

- 3

$- 3$ to the left of

r

$r$ .

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

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

Step 2.1.3

Multiply

5

$5$ by

- 3

$- 3$ .

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

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

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

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

Step 2.2

Add

- 3 r

$- 3 r$ and

5 r

$5 r$ .

r^{2} + 2 r - 15

$r^{2} + 2 r - 15$

r^{2} + 2 r - 15

$r^{2} + 2 r - 15$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$