Algebra Examples

(a + 5) (a - 5)

$(a + 5) (a - 5)$

Step 1

Expand

(a + 5) (a - 5)

$(a + 5) (a - 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

a (a - 5) + 5 (a - 5)

$a (a - 5) + 5 (a - 5)$

Step 1.2

Apply the distributive property.

a \cdot a + a \cdot - 5 + 5 (a - 5)

$a \cdot a + a \cdot - 5 + 5 (a - 5)$

Step 1.3

Apply the distributive property.

a \cdot a + a \cdot - 5 + 5 a + 5 \cdot - 5

$a \cdot a + a \cdot - 5 + 5 a + 5 \cdot - 5$

a \cdot a + a \cdot - 5 + 5 a + 5 \cdot - 5

$a \cdot a + a \cdot - 5 + 5 a + 5 \cdot - 5$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

a \cdot a + a \cdot - 5 + 5 a + 5 \cdot - 5

$a \cdot a + a \cdot - 5 + 5 a + 5 \cdot - 5$ .

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Step 2.1.1

Reorder the factors in the terms

a \cdot - 5

$a \cdot - 5$ and

5 a

$5 a$ .

a \cdot a - 5 a + 5 a + 5 \cdot - 5

$a \cdot a - 5 a + 5 a + 5 \cdot - 5$

Step 2.1.2

Add

- 5 a

$- 5 a$ and

5 a

$5 a$ .

a \cdot a + 0 + 5 \cdot - 5

$a \cdot a + 0 + 5 \cdot - 5$

Step 2.1.3

Add

a \cdot a

$a \cdot a$ and

0

$0$ .

a \cdot a + 5 \cdot - 5

$a \cdot a + 5 \cdot - 5$

a \cdot a + 5 \cdot - 5

$a \cdot a + 5 \cdot - 5$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply

a

$a$ by

a

$a$ .

a^{2} + 5 \cdot - 5

$a^{2} + 5 \cdot - 5$

Step 2.2.2

Multiply

5

$5$ by

- 5

$- 5$ .

a^{2} - 25

$a^{2} - 25$

a^{2} - 25

$a^{2} - 25$

a^{2} - 25

$a^{2} - 25$

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

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