Calculus Examples

{(1 - t)}^{2}

${(1 - t)}^{2}$

Step 1

Rewrite

{(1 - t)}^{2}

${(1 - t)}^{2}$ as

(1 - t) (1 - t)

$(1 - t) (1 - t)$ .

(1 - t) (1 - t)

$(1 - t) (1 - t)$

Step 2

Expand

(1 - t) (1 - t)

$(1 - t) (1 - t)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

1 (1 - t) - t (1 - t)

$1 (1 - t) - t (1 - t)$

Step 2.2

Apply the distributive property.

1 \cdot 1 + 1 (- t) - t (1 - t)

$1 \cdot 1 + 1 (- t) - t (1 - t)$

Step 2.3

Apply the distributive property.

1 \cdot 1 + 1 (- t) - t \cdot 1 - t (- t)

$1 \cdot 1 + 1 (- t) - t \cdot 1 - t (- t)$

1 \cdot 1 + 1 (- t) - t \cdot 1 - t (- t)

$1 \cdot 1 + 1 (- t) - t \cdot 1 - t (- t)$

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

1

$1$ by

1

$1$ .

1 + 1 (- t) - t \cdot 1 - t (- t)

$1 + 1 (- t) - t \cdot 1 - t (- t)$

Step 3.1.2

Multiply

- t

$- t$ by

1

$1$ .

1 - t - t \cdot 1 - t (- t)

$1 - t - t \cdot 1 - t (- t)$

Step 3.1.3

Multiply

- 1

$- 1$ by

1

$1$ .

1 - t - t - t (- t)

$1 - t - t - t (- t)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

1 - t - t - 1 \cdot - 1 t \cdot t

$1 - t - t - 1 \cdot - 1 t \cdot t$

Step 3.1.5

Multiply

t

$t$ by

t

$t$ by adding the exponents.

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Step 3.1.5.1

Move

t

$t$ .

1 - t - t - 1 \cdot - 1 (t \cdot t)

$1 - t - t - 1 \cdot - 1 (t \cdot t)$

Step 3.1.5.2

Multiply

t

$t$ by

t

$t$ .

1 - t - t - 1 \cdot - 1 t^{2}

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

1 - t - t - 1 \cdot - 1 t^{2}

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

Step 3.1.6

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

1 - t - t + 1 t^{2}

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

Step 3.1.7

Multiply

t^{2}

$t^{2}$ by

1

$1$ .

1 - t - t + t^{2}

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

1 - t - t + t^{2}

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

Step 3.2

Subtract

t

$t$ from

- t

$- t$ .

1 - 2 t + t^{2}

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

1 - 2 t + t^{2}

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

{(1 - t)}^{2}

${(1 - t)}^{2}$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$