Algebra Examples

$(x + 2) (x + 3) = (x + 1) (x + 5)$

Step 1

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

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Step 1.1

Rewrite.

$0 + 0 + (x + 2) (x + 3) = (x + 1) (x + 5)$

Step 1.2

Simplify by adding zeros.

$(x + 2) (x + 3) = (x + 1) (x + 5)$

Step 1.3

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

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Step 1.3.1

Apply the distributive property.

$x (x + 3) + 2 (x + 3) = (x + 1) (x + 5)$

Step 1.3.2

Apply the distributive property.

$x \cdot x + x \cdot 3 + 2 (x + 3) = (x + 1) (x + 5)$

Step 1.3.3

Apply the distributive property.

$x \cdot x + x \cdot 3 + 2 x + 2 \cdot 3 = (x + 1) (x + 5)$

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 $x$ .

$x^{2} + x \cdot 3 + 2 x + 2 \cdot 3 = (x + 1) (x + 5)$

Step 1.4.1.2

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

$x^{2} + 3 \cdot x + 2 x + 2 \cdot 3 = (x + 1) (x + 5)$

Step 1.4.1.3

Multiply $2$ by $3$ .

$x^{2} + 3 x + 2 x + 6 = (x + 1) (x + 5)$

Step 1.4.2

Add $3 x$ and $2 x$ .

$x^{2} + 5 x + 6 = (x + 1) (x + 5)$

Step 2

Simplify $(x + 1) (x + 5)$ .

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Step 2.1

Expand $(x + 1) (x + 5)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$x^{2} + 5 x + 6 = x (x + 5) + 1 (x + 5)$

Step 2.1.2

Apply the distributive property.

$x^{2} + 5 x + 6 = x \cdot x + x \cdot 5 + 1 (x + 5)$

Step 2.1.3

Apply the distributive property.

$x^{2} + 5 x + 6 = x \cdot x + x \cdot 5 + 1 x + 1 \cdot 5$

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Multiply $x$ by $x$ .

$x^{2} + 5 x + 6 = x^{2} + x \cdot 5 + 1 x + 1 \cdot 5$

Step 2.2.1.2

Move $5$ to the left of $x$ .

$x^{2} + 5 x + 6 = x^{2} + 5 \cdot x + 1 x + 1 \cdot 5$

Step 2.2.1.3

Multiply $x$ by $1$ .

$x^{2} + 5 x + 6 = x^{2} + 5 x + x + 1 \cdot 5$

Step 2.2.1.4

Multiply $5$ by $1$ .

$x^{2} + 5 x + 6 = x^{2} + 5 x + x + 5$

Step 2.2.2

Add $5 x$ and $x$ .

$x^{2} + 5 x + 6 = x^{2} + 6 x + 5$

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.

$x^{2} + 5 x + 6 - x^{2} = 6 x + 5$

Step 3.2

Subtract $6 x$ from both sides of the equation.

$x^{2} + 5 x + 6 - x^{2} - 6 x = 5$

Step 3.3

Combine the opposite terms in $x^{2} + 5 x + 6 - x^{2} - 6 x$ .

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Step 3.3.1

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

$5 x + 6 + 0 - 6 x = 5$

Step 3.3.2

Add $5 x + 6$ and $0$ .

$5 x + 6 - 6 x = 5$

Step 3.4

Subtract $6 x$ from $5 x$ .

$- x + 6 = 5$

Step 4

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

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Step 4.1

Subtract $6$ from both sides of the equation.

$- x = 5 - 6$

Step 4.2

Subtract $6$ from $5$ .

$- x = - 1$

Step 5

Divide each term in $- x = - 1$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- x = - 1$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 1}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 1}{- 1}$

Step 5.2.2

Divide $x$ by $1$ .

$x = \frac{- 1}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 1$ by $- 1$ .

$x = 1$