Algebra Examples

$(x^{2} - 3 x + 9) (x + 3)$

Step 1

Expand $(x^{2} - 3 x + 9) (x + 3)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x + x^{2} \cdot 3 - 3 x \cdot x - 3 x \cdot 3 + 9 x + 9 \cdot 3$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

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Step 2.1.1.1.1

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

$x^{2} x^{1} + x^{2} \cdot 3 - 3 x \cdot x - 3 x \cdot 3 + 9 x + 9 \cdot 3$

Step 2.1.1.1.2

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

$x^{2 + 1} + x^{2} \cdot 3 - 3 x \cdot x - 3 x \cdot 3 + 9 x + 9 \cdot 3$

Step 2.1.1.2

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot 3 - 3 x \cdot x - 3 x \cdot 3 + 9 x + 9 \cdot 3$

Step 2.1.2

Move $3$ to the left of $x^{2}$ .

$x^{3} + 3 \cdot x^{2} - 3 x \cdot x - 3 x \cdot 3 + 9 x + 9 \cdot 3$

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

$x^{3} + 3 x^{2} - 3 (x \cdot x) - 3 x \cdot 3 + 9 x + 9 \cdot 3$

Step 2.1.3.2

Multiply $x$ by $x$ .

$x^{3} + 3 x^{2} - 3 x^{2} - 3 x \cdot 3 + 9 x + 9 \cdot 3$

Step 2.1.4

Multiply $3$ by $- 3$ .

$x^{3} + 3 x^{2} - 3 x^{2} - 9 x + 9 x + 9 \cdot 3$

Step 2.1.5

Multiply $9$ by $3$ .

$x^{3} + 3 x^{2} - 3 x^{2} - 9 x + 9 x + 27$

Step 2.2

Combine the opposite terms in $x^{3} + 3 x^{2} - 3 x^{2} - 9 x + 9 x + 27$ .

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Step 2.2.1

Subtract $3 x^{2}$ from $3 x^{2}$ .

$x^{3} + 0 - 9 x + 9 x + 27$

Step 2.2.2

Add $x^{3}$ and $0$ .

$x^{3} - 9 x + 9 x + 27$

Step 2.2.3

Add $- 9 x$ and $9 x$ .

$x^{3} + 0 + 27$

Step 2.2.4

Add $x^{3}$ and $0$ .

$x^{3} + 27$