Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $5 x (5 x) + 5 x \cdot - 1 + 1 (5 x) + 1 \cdot - 1$ .

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Step 2.1.1

Reorder the factors in the terms $5 x \cdot - 1$ and $1 (5 x)$ .

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

Step 2.1.2

Add $- 1 \cdot 5 x$ and $1 \cdot 5 x$ .

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

Step 2.1.3

Add $5 x (5 x)$ and $0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2.2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.2.2.1

Move $x$ .

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

Step 2.2.2.2

Multiply $x$ by $x$ .

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

Step 2.2.3

Multiply $5$ by $5$ .

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

Step 2.2.4

Multiply $- 1$ by $1$ .

$25 x^{2} - 1$