Algebra Examples

$(x - 4) (x^{2} - 2 x - 3)$

Step 1

Expand $(x - 4) (x^{2} - 2 x - 3)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x^{2} + x (- 2 x) + x \cdot - 3 - 4 x^{2} - 4 (- 2 x) - 4 \cdot - 3$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

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Step 2.1.1.1.1

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

$x^{1} x^{2} + x (- 2 x) + x \cdot - 3 - 4 x^{2} - 4 (- 2 x) - 4 \cdot - 3$

Step 2.1.1.1.2

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

$x^{1 + 2} + x (- 2 x) + x \cdot - 3 - 4 x^{2} - 4 (- 2 x) - 4 \cdot - 3$

Step 2.1.1.2

Add $1$ and $2$ .

$x^{3} + x (- 2 x) + x \cdot - 3 - 4 x^{2} - 4 (- 2 x) - 4 \cdot - 3$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$x^{3} - 2 x \cdot x + x \cdot - 3 - 4 x^{2} - 4 (- 2 x) - 4 \cdot - 3$

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

$x^{3} - 2 (x \cdot x) + x \cdot - 3 - 4 x^{2} - 4 (- 2 x) - 4 \cdot - 3$

Step 2.1.3.2

Multiply $x$ by $x$ .

$x^{3} - 2 x^{2} + x \cdot - 3 - 4 x^{2} - 4 (- 2 x) - 4 \cdot - 3$

Step 2.1.4

Move $- 3$ to the left of $x$ .

$x^{3} - 2 x^{2} - 3 \cdot x - 4 x^{2} - 4 (- 2 x) - 4 \cdot - 3$

Step 2.1.5

Multiply $- 2$ by $- 4$ .

$x^{3} - 2 x^{2} - 3 x - 4 x^{2} + 8 x - 4 \cdot - 3$

Step 2.1.6

Multiply $- 4$ by $- 3$ .

$x^{3} - 2 x^{2} - 3 x - 4 x^{2} + 8 x + 12$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $4 x^{2}$ from $- 2 x^{2}$ .

$x^{3} - 6 x^{2} - 3 x + 8 x + 12$

Step 2.2.2

Add $- 3 x$ and $8 x$ .

$x^{3} - 6 x^{2} + 5 x + 12$