Algebra Examples

$(1 - 6 x) (x^{2} - 4)$

Step 1

Expand $(1 - 6 x) (x^{2} - 4)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$1 (x^{2} - 4) - 6 x (x^{2} - 4)$

Step 1.2

Apply the distributive property.

$1 x^{2} + 1 \cdot - 4 - 6 x (x^{2} - 4)$

Step 1.3

Apply the distributive property.

$1 x^{2} + 1 \cdot - 4 - 6 x \cdot x^{2} - 6 x \cdot - 4$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x^{2}$ by $1$ .

$x^{2} + 1 \cdot - 4 - 6 x \cdot x^{2} - 6 x \cdot - 4$

Step 2.1.2

Multiply $- 4$ by $1$ .

$x^{2} - 4 - 6 x \cdot x^{2} - 6 x \cdot - 4$

Step 2.1.3

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 2.1.3.1

Move $x^{2}$ .

$x^{2} - 4 - 6 (x^{2} x) - 6 x \cdot - 4$

Step 2.1.3.2

Multiply $x^{2}$ by $x$ .

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Step 2.1.3.2.1

Raise $x$ to the power of $1$ .

$x^{2} - 4 - 6 (x^{2} x^{1}) - 6 x \cdot - 4$

Step 2.1.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} - 4 - 6 x^{2 + 1} - 6 x \cdot - 4$

Step 2.1.3.3

Add $2$ and $1$ .

$x^{2} - 4 - 6 x^{3} - 6 x \cdot - 4$

Step 2.1.4

Multiply $- 4$ by $- 6$ .

$x^{2} - 4 - 6 x^{3} + 24 x$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $- 4$ .

$x^{2} - 6 x^{3} + 24 x - 4$

Step 2.2.2

Reorder $x^{2}$ and $- 6 x^{3}$ .

$- 6 x^{3} + x^{2} + 24 x - 4$