Basic Math Examples

${(m - t)}^{2} - w^{2}$

Step 1

Rewrite ${(m - t)}^{2}$ as $(m - t) (m - t)$ .

$(m - t) (m - t) - w^{2}$

Step 2

Expand $(m - t) (m - t)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$m (m - t) - t (m - t) - w^{2}$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $m$ by $m$ .

$m^{2} + m (- t) - t m - t (- t) - w^{2}$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$m^{2} - m t - t m - t (- t) - w^{2}$

Step 3.1.3

Rewrite using the commutative property of multiplication.

$m^{2} - m t - t m - 1 \cdot - 1 t \cdot t - w^{2}$

Step 3.1.4

Multiply $t$ by $t$ by adding the exponents.

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Step 3.1.4.1

Move $t$ .

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

Step 3.1.4.2

Multiply $t$ by $t$ .

$m^{2} - m t - t m - 1 \cdot - 1 t^{2} - w^{2}$

Step 3.1.5

Multiply $- 1$ by $- 1$ .

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

Step 3.1.6

Multiply $t^{2}$ by $1$ .

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

Step 3.2

Subtract $t m$ from $- m t$ .

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Step 3.2.1

Move $t$ .

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

Step 3.2.2

Subtract $m t$ from $- m t$ .

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