Precalculus Examples

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

Step 1

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$(x + 2) ((x - 3) (x - 3))$

Step 2

Expand $(x - 3) (x - 3)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$(x + 2) (x (x - 3) - 3 (x - 3))$

Step 2.2

Apply the distributive property.

$(x + 2) (x \cdot x + x \cdot - 3 - 3 (x - 3))$

Step 2.3

Apply the distributive property.

$(x + 2) (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

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

Step 3.1.2

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

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

Step 3.1.3

Multiply $- 3$ by $- 3$ .

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

Step 3.2

Subtract $3 x$ from $- 3 x$ .

$(x + 2) (x^{2} - 6 x + 9)$

Step 4

Expand $(x + 2) (x^{2} - 6 x + 9)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x^{2} + x (- 6 x) + x \cdot 9 + 2 x^{2} + 2 (- 6 x) + 2 \cdot 9$

Step 5

Simplify terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

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

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Step 5.1.1.1

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

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Step 5.1.1.1.1

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

$x^{1} x^{2} + x (- 6 x) + x \cdot 9 + 2 x^{2} + 2 (- 6 x) + 2 \cdot 9$

Step 5.1.1.1.2

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

$x^{1 + 2} + x (- 6 x) + x \cdot 9 + 2 x^{2} + 2 (- 6 x) + 2 \cdot 9$

Step 5.1.1.2

Add $1$ and $2$ .

$x^{3} + x (- 6 x) + x \cdot 9 + 2 x^{2} + 2 (- 6 x) + 2 \cdot 9$

Step 5.1.2

Rewrite using the commutative property of multiplication.

$x^{3} - 6 x \cdot x + x \cdot 9 + 2 x^{2} + 2 (- 6 x) + 2 \cdot 9$

Step 5.1.3

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

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Step 5.1.3.1

Move $x$ .

$x^{3} - 6 (x \cdot x) + x \cdot 9 + 2 x^{2} + 2 (- 6 x) + 2 \cdot 9$

Step 5.1.3.2

Multiply $x$ by $x$ .

$x^{3} - 6 x^{2} + x \cdot 9 + 2 x^{2} + 2 (- 6 x) + 2 \cdot 9$

Step 5.1.4

Move $9$ to the left of $x$ .

$x^{3} - 6 x^{2} + 9 \cdot x + 2 x^{2} + 2 (- 6 x) + 2 \cdot 9$

Step 5.1.5

Multiply $- 6$ by $2$ .

$x^{3} - 6 x^{2} + 9 x + 2 x^{2} - 12 x + 2 \cdot 9$

Step 5.1.6

Multiply $2$ by $9$ .

$x^{3} - 6 x^{2} + 9 x + 2 x^{2} - 12 x + 18$

Step 5.2

Simplify by adding terms.

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Step 5.2.1

Add $- 6 x^{2}$ and $2 x^{2}$ .

$x^{3} - 4 x^{2} + 9 x - 12 x + 18$

Step 5.2.2

Subtract $12 x$ from $9 x$ .

$x^{3} - 4 x^{2} - 3 x + 18$