Algebra Examples

(5 x - 4) (5 x + 4)

$(5 x - 4) (5 x + 4)$

Step 1

Expand

(5 x - 4) (5 x + 4)

$(5 x - 4) (5 x + 4)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

5 x (5 x + 4) - 4 (5 x + 4)

$5 x (5 x + 4) - 4 (5 x + 4)$

Step 1.2

Apply the distributive property.

5 x (5 x) + 5 x \cdot 4 - 4 (5 x + 4)

$5 x (5 x) + 5 x \cdot 4 - 4 (5 x + 4)$

Step 1.3

Apply the distributive property.

5 x (5 x) + 5 x \cdot 4 - 4 (5 x) - 4 \cdot 4

$5 x (5 x) + 5 x \cdot 4 - 4 (5 x) - 4 \cdot 4$

5 x (5 x) + 5 x \cdot 4 - 4 (5 x) - 4 \cdot 4

$5 x (5 x) + 5 x \cdot 4 - 4 (5 x) - 4 \cdot 4$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

5 x (5 x) + 5 x \cdot 4 - 4 (5 x) - 4 \cdot 4

$5 x (5 x) + 5 x \cdot 4 - 4 (5 x) - 4 \cdot 4$ .

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Step 2.1.1

Reorder the factors in the terms

5 x \cdot 4

$5 x \cdot 4$ and

- 4 (5 x)

$- 4 (5 x)$ .

5 x (5 x) + 4 \cdot 5 x - 4 \cdot 5 x - 4 \cdot 4

$5 x (5 x) + 4 \cdot 5 x - 4 \cdot 5 x - 4 \cdot 4$

Step 2.1.2

Subtract

4 \cdot 5 x

$4 \cdot 5 x$ from

4 \cdot 5 x

$4 \cdot 5 x$ .

5 x (5 x) + 0 - 4 \cdot 4

$5 x (5 x) + 0 - 4 \cdot 4$

Step 2.1.3

Add

5 x (5 x)

$5 x (5 x)$ and

0

$0$ .

5 x (5 x) - 4 \cdot 4

$5 x (5 x) - 4 \cdot 4$

5 x (5 x) - 4 \cdot 4

$5 x (5 x) - 4 \cdot 4$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

5 \cdot 5 x \cdot x - 4 \cdot 4

$5 \cdot 5 x \cdot x - 4 \cdot 4$

Step 2.2.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.2.2.1

Move

x

$x$ .

5 \cdot 5 (x \cdot x) - 4 \cdot 4

$5 \cdot 5 (x \cdot x) - 4 \cdot 4$

Step 2.2.2.2

Multiply

x

$x$ by

x

$x$ .

5 \cdot 5 x^{2} - 4 \cdot 4

$5 \cdot 5 x^{2} - 4 \cdot 4$

5 \cdot 5 x^{2} - 4 \cdot 4

$5 \cdot 5 x^{2} - 4 \cdot 4$

Step 2.2.3

Multiply

5

$5$ by

5

$5$ .

25 x^{2} - 4 \cdot 4

$25 x^{2} - 4 \cdot 4$

Step 2.2.4

Multiply

- 4

$- 4$ by

4

$4$ .

25 x^{2} - 16

$25 x^{2} - 16$

25 x^{2} - 16

$25 x^{2} - 16$

25 x^{2} - 16

$25 x^{2} - 16$

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

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