Algebra Examples

$(m + 2) (m + 3) = (m + 2) (m - 2)$

Step 1

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

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Step 1.1

Rewrite.

$0 + 0 + (m + 2) (m + 3) = (m + 2) (m - 2)$

Step 1.2

Simplify by adding zeros.

$(m + 2) (m + 3) = (m + 2) (m - 2)$

Step 1.3

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

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Step 1.3.1

Apply the distributive property.

$m (m + 3) + 2 (m + 3) = (m + 2) (m - 2)$

Step 1.3.2

Apply the distributive property.

$m \cdot m + m \cdot 3 + 2 (m + 3) = (m + 2) (m - 2)$

Step 1.3.3

Apply the distributive property.

$m \cdot m + m \cdot 3 + 2 m + 2 \cdot 3 = (m + 2) (m - 2)$

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 $m$ by $m$ .

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

Step 1.4.1.2

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

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

Step 1.4.1.3

Multiply $2$ by $3$ .

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

Step 1.4.2

Add $3 m$ and $2 m$ .

$m^{2} + 5 m + 6 = (m + 2) (m - 2)$

Step 2

Simplify $(m + 2) (m - 2)$ .

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Step 2.1

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

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Step 2.1.1

Apply the distributive property.

$m^{2} + 5 m + 6 = m (m - 2) + 2 (m - 2)$

Step 2.1.2

Apply the distributive property.

$m^{2} + 5 m + 6 = m \cdot m + m \cdot - 2 + 2 (m - 2)$

Step 2.1.3

Apply the distributive property.

$m^{2} + 5 m + 6 = m \cdot m + m \cdot - 2 + 2 m + 2 \cdot - 2$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the opposite terms in $m \cdot m + m \cdot - 2 + 2 m + 2 \cdot - 2$ .

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Step 2.2.1.1

Reorder the factors in the terms $m \cdot - 2$ and $2 m$ .

$m^{2} + 5 m + 6 = m \cdot m - 2 m + 2 m + 2 \cdot - 2$

Step 2.2.1.2

Add $- 2 m$ and $2 m$ .

$m^{2} + 5 m + 6 = m \cdot m + 0 + 2 \cdot - 2$

Step 2.2.1.3

Add $m \cdot m$ and $0$ .

$m^{2} + 5 m + 6 = m \cdot m + 2 \cdot - 2$

Step 2.2.2

Simplify each term.

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Step 2.2.2.1

Multiply $m$ by $m$ .

$m^{2} + 5 m + 6 = m^{2} + 2 \cdot - 2$

Step 2.2.2.2

Multiply $2$ by $- 2$ .

$m^{2} + 5 m + 6 = m^{2} - 4$

Step 3

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

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Step 3.1

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

$m^{2} + 5 m + 6 - m^{2} = - 4$

Step 3.2

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

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Step 3.2.1

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

$5 m + 6 + 0 = - 4$

Step 3.2.2

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

$5 m + 6 = - 4$

Step 4

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

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Step 4.1

Subtract $6$ from both sides of the equation.

$5 m = - 4 - 6$

Step 4.2

Subtract $6$ from $- 4$ .

$5 m = - 10$

Step 5

Divide each term in $5 m = - 10$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 m = - 10$ by $5$ .

$\frac{5 m}{5} = \frac{- 10}{5}$

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.

$\frac{5 m}{5} = \frac{- 10}{5}$

Step 5.2.1.2

Divide $m$ by $1$ .

$m = \frac{- 10}{5}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 10$ by $5$ .

$m = - 2$