Precalculus Examples

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

Step 1

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

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Step 1.1

Rewrite.

$0 + 0 + (x + 2) (x - 3) = {(x - 3)}^{2}$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Expand $(x + 2) (x - 3)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

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

Step 1.3.2

Apply the distributive property.

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

Step 1.3.3

Apply the distributive property.

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

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $x$ by $x$ .

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

Step 1.4.1.2

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

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

Step 1.4.1.3

Multiply $2$ by $- 3$ .

$x^{2} - 3 x + 2 x - 6 = {(x - 3)}^{2}$

Step 1.4.2

Add $- 3 x$ and $2 x$ .

$x^{2} - x - 6 = {(x - 3)}^{2}$

Step 2

Simplify ${(x - 3)}^{2}$ .

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Step 2.1

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

$x^{2} - x - 6 = (x - 3) (x - 3)$

Step 2.2

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

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Step 2.2.1

Apply the distributive property.

$x^{2} - x - 6 = x (x - 3) - 3 (x - 3)$

Step 2.2.2

Apply the distributive property.

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

Step 2.2.3

Apply the distributive property.

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

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $x$ by $x$ .

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

Step 2.3.1.2

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

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

Step 2.3.1.3

Multiply $- 3$ by $- 3$ .

$x^{2} - x - 6 = x^{2} - 3 x - 3 x + 9$

Step 2.3.2

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

$x^{2} - x - 6 = x^{2} - 6 x + 9$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $x^{2}$ from both sides of the equation.

$x^{2} - x - 6 - x^{2} = - 6 x + 9$

Step 3.2

Add $6 x$ to both sides of the equation.

$x^{2} - x - 6 - x^{2} + 6 x = 9$

Step 3.3

Combine the opposite terms in $x^{2} - x - 6 - x^{2} + 6 x$ .

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Step 3.3.1

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

$- x - 6 + 0 + 6 x = 9$

Step 3.3.2

Add $- x - 6$ and $0$ .

$- x - 6 + 6 x = 9$

Step 3.4

Add $- x$ and $6 x$ .

$5 x - 6 = 9$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Add $6$ to both sides of the equation.

$5 x = 9 + 6$

Step 4.2

Add $9$ and $6$ .

$5 x = 15$

Step 5

Divide each term in $5 x = 15$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 x = 15$ by $5$ .

$\frac{5 x}{5} = \frac{15}{5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{15}{5}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{5}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $15$ by $5$ .

$x = 3$