Basic Math Examples

$(m + 1) (m - 1) + {(m + 1)}^{2} - 2 m$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Expand $(m + 1) (m - 1)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$m (m - 1) + 1 (m - 1) + {(m + 1)}^{2} - 2 m$

Step 1.1.2

Apply the distributive property.

$m \cdot m + m \cdot - 1 + 1 (m - 1) + {(m + 1)}^{2} - 2 m$

Step 1.1.3

Apply the distributive property.

$m \cdot m + m \cdot - 1 + 1 m + 1 \cdot - 1 + {(m + 1)}^{2} - 2 m$

Step 1.2

Simplify and combine like terms.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Multiply $m$ by $m$ .

$m^{2} + m \cdot - 1 + 1 m + 1 \cdot - 1 + {(m + 1)}^{2} - 2 m$

Step 1.2.1.2

Move $- 1$ to the left of $m$ .

$m^{2} - 1 \cdot m + 1 m + 1 \cdot - 1 + {(m + 1)}^{2} - 2 m$

Step 1.2.1.3

Rewrite $- 1 m$ as $- m$ .

$m^{2} - m + 1 m + 1 \cdot - 1 + {(m + 1)}^{2} - 2 m$

Step 1.2.1.4

Multiply $m$ by $1$ .

$m^{2} - m + m + 1 \cdot - 1 + {(m + 1)}^{2} - 2 m$

Step 1.2.1.5

Multiply $- 1$ by $1$ .

$m^{2} - m + m - 1 + {(m + 1)}^{2} - 2 m$

Step 1.2.2

Add $- m$ and $m$ .

$m^{2} + 0 - 1 + {(m + 1)}^{2} - 2 m$

Step 1.2.3

Add $m^{2}$ and $0$ .

$m^{2} - 1 + {(m + 1)}^{2} - 2 m$

Step 1.3

Rewrite ${(m + 1)}^{2}$ as $(m + 1) (m + 1)$ .

$m^{2} - 1 + (m + 1) (m + 1) - 2 m$

Step 1.4

Expand $(m + 1) (m + 1)$ using the FOIL Method.

Tap for more steps...

Step 1.4.1

Apply the distributive property.

$m^{2} - 1 + m (m + 1) + 1 (m + 1) - 2 m$

Step 1.4.2

Apply the distributive property.

$m^{2} - 1 + m \cdot m + m \cdot 1 + 1 (m + 1) - 2 m$

Step 1.4.3

Apply the distributive property.

$m^{2} - 1 + m \cdot m + m \cdot 1 + 1 m + 1 \cdot 1 - 2 m$

Step 1.5

Simplify and combine like terms.

Tap for more steps...

Step 1.5.1

Simplify each term.

Tap for more steps...

Step 1.5.1.1

Multiply $m$ by $m$ .

$m^{2} - 1 + m^{2} + m \cdot 1 + 1 m + 1 \cdot 1 - 2 m$

Step 1.5.1.2

Multiply $m$ by $1$ .

$m^{2} - 1 + m^{2} + m + 1 m + 1 \cdot 1 - 2 m$

Step 1.5.1.3

Multiply $m$ by $1$ .

$m^{2} - 1 + m^{2} + m + m + 1 \cdot 1 - 2 m$

Step 1.5.1.4

Multiply $1$ by $1$ .

$m^{2} - 1 + m^{2} + m + m + 1 - 2 m$

Step 1.5.2

Add $m$ and $m$ .

$m^{2} - 1 + m^{2} + 2 m + 1 - 2 m$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Combine the opposite terms in $m^{2} - 1 + m^{2} + 2 m + 1 - 2 m$ .

Tap for more steps...

Step 2.1.1

Add $- 1$ and $1$ .

$m^{2} + m^{2} + 2 m + 0 - 2 m$

Step 2.1.2

Add $m^{2} + m^{2} + 2 m$ and $0$ .

$m^{2} + m^{2} + 2 m - 2 m$

Step 2.1.3

Subtract $2 m$ from $2 m$ .

$m^{2} + m^{2} + 0$

Step 2.1.4

Add $m^{2} + m^{2}$ and $0$ .

$m^{2} + m^{2}$

Step 2.2

Add $m^{2}$ and $m^{2}$ .

$2 m^{2}$