Algebra Examples

$6 (x^{2} - 1) \cdot \frac{6 x - 1}{6 (x + 1)}$

Step 1

Simplify terms.

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Step 1.1

Cancel the common factor of $6$ .

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Step 1.1.1

Cancel the common factor.

$6 (x^{2} - 1) \cdot \frac{6 x - 1}{6 (x + 1)}$

Step 1.1.2

Rewrite the expression.

$(x^{2} - 1) \cdot \frac{6 x - 1}{x + 1}$

Step 1.2

Multiply $x^{2} - 1$ by $\frac{6 x - 1}{x + 1}$ .

$\frac{(x^{2} - 1) (6 x - 1)}{x + 1}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$\frac{(x^{2} - 1^{2}) (6 x - 1)}{x + 1}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$\frac{(x + 1) (x - 1) (6 x - 1)}{x + 1}$

Step 3

Cancel the common factor of $x + 1$ .

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Step 3.1

Cancel the common factor.

$\frac{(x + 1) (x - 1) (6 x - 1)}{x + 1}$

Step 3.2

Divide $(x - 1) (6 x - 1)$ by $1$ .

$(x - 1) (6 x - 1)$

Step 4

Expand $(x - 1) (6 x - 1)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$x (6 x - 1) - 1 (6 x - 1)$

Step 4.2

Apply the distributive property.

$x (6 x) + x \cdot - 1 - 1 (6 x - 1)$

Step 4.3

Apply the distributive property.

$x (6 x) + x \cdot - 1 - 1 (6 x) - 1 \cdot - 1$

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Rewrite using the commutative property of multiplication.

$6 x \cdot x + x \cdot - 1 - 1 (6 x) - 1 \cdot - 1$

Step 5.1.2

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

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Step 5.1.2.1

Move $x$ .

$6 (x \cdot x) + x \cdot - 1 - 1 (6 x) - 1 \cdot - 1$

Step 5.1.2.2

Multiply $x$ by $x$ .

$6 x^{2} + x \cdot - 1 - 1 (6 x) - 1 \cdot - 1$

Step 5.1.3

Move $- 1$ to the left of $x$ .

$6 x^{2} - 1 \cdot x - 1 (6 x) - 1 \cdot - 1$

Step 5.1.4

Rewrite $- 1 x$ as $- x$ .

$6 x^{2} - x - 1 (6 x) - 1 \cdot - 1$

Step 5.1.5

Multiply $6$ by $- 1$ .

$6 x^{2} - x - 6 x - 1 \cdot - 1$

Step 5.1.6

Multiply $- 1$ by $- 1$ .

$6 x^{2} - x - 6 x + 1$

Step 5.2

Subtract $6 x$ from $- x$ .

$6 x^{2} - 7 x + 1$