Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Use the Binomial Theorem.

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

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $3$ by $3$ .

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

Step 1.2.2

Multiply $3$ by $3^{2}$ by adding the exponents.

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Step 1.2.2.1

Move $3^{2}$ .

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

Step 1.2.2.2

Multiply $3^{2}$ by $3$ .

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Step 1.2.2.2.1

Raise $3$ to the power of $1$ .

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

Step 1.2.2.2.2

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

$x^{3} + 9 x^{2} + 3^{2 + 1} x + 3^{3} - 9 x (x + 3)$

Step 1.2.2.3

Add $2$ and $1$ .

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

Step 1.2.3

Raise $3$ to the power of $3$ .

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

Step 1.2.4

Raise $3$ to the power of $3$ .

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

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Step 1.4.1

Move $x$ .

$x^{3} + 9 x^{2} + 27 x + 27 - 9 (x \cdot x) - 9 x \cdot 3$

Step 1.4.2

Multiply $x$ by $x$ .

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

Step 1.5

Multiply $3$ by $- 9$ .

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

Step 2

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

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Step 2.1

Subtract $9 x^{2}$ from $9 x^{2}$ .

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

Step 2.2

Add $x^{3} + 27 x + 27$ and $0$ .

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

Step 2.3

Subtract $27 x$ from $27 x$ .

$x^{3} + 0 + 27$

Step 2.4

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

$x^{3} + 27$