Algebra Examples

(5 x + 1) (5 x - 1)

$(5 x + 1) (5 x - 1)$

Step 1

Expand

(5 x + 1) (5 x - 1)

$(5 x + 1) (5 x - 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

5 x (5 x - 1) + 1 (5 x - 1)

$5 x (5 x - 1) + 1 (5 x - 1)$

Step 1.2

Apply the distributive property.

5 x (5 x) + 5 x \cdot - 1 + 1 (5 x - 1)

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

Step 1.3

Apply the distributive property.

5 x (5 x) + 5 x \cdot - 1 + 1 (5 x) + 1 \cdot - 1

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

5 x (5 x) + 5 x \cdot - 1 + 1 (5 x) + 1 \cdot - 1

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

5 x (5 x) + 5 x \cdot - 1 + 1 (5 x) + 1 \cdot - 1

$5 x (5 x) + 5 x \cdot - 1 + 1 (5 x) + 1 \cdot - 1$ .

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Step 2.1.1

Reorder the factors in the terms

5 x \cdot - 1

$5 x \cdot - 1$ and

1 (5 x)

$1 (5 x)$ .

5 x (5 x) - 1 \cdot 5 x + 1 \cdot 5 x + 1 \cdot - 1

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

Step 2.1.2

Add

- 1 \cdot 5 x

$- 1 \cdot 5 x$ and

1 \cdot 5 x

$1 \cdot 5 x$ .

5 x (5 x) + 0 + 1 \cdot - 1

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

Step 2.1.3

Add

5 x (5 x)

$5 x (5 x)$ and

0

$0$ .

5 x (5 x) + 1 \cdot - 1

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

5 x (5 x) + 1 \cdot - 1

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

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 + 1 \cdot - 1

$5 \cdot 5 x \cdot x + 1 \cdot - 1$

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) + 1 \cdot - 1

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

Step 2.2.2.2

Multiply

x

$x$ by

x

$x$ .

5 \cdot 5 x^{2} + 1 \cdot - 1

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

5 \cdot 5 x^{2} + 1 \cdot - 1

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

Step 2.2.3

Multiply

5

$5$ by

5

$5$ .

25 x^{2} + 1 \cdot - 1

$25 x^{2} + 1 \cdot - 1$

Step 2.2.4

Multiply

- 1

$- 1$ by

1

$1$ .

25 x^{2} - 1

$25 x^{2} - 1$

25 x^{2} - 1

$25 x^{2} - 1$

25 x^{2} - 1

$25 x^{2} - 1$