Basic Math Examples

{(c - d)}^{2}

${(c - d)}^{2}$

Step 1

Rewrite

{(c - d)}^{2}

${(c - d)}^{2}$ as

(c - d) (c - d)

$(c - d) (c - d)$ .

(c - d) (c - d)

$(c - d) (c - d)$

Step 2

Expand

(c - d) (c - d)

$(c - d) (c - d)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

c (c - d) - d (c - d)

$c (c - d) - d (c - d)$

Step 2.2

Apply the distributive property.

c \cdot c + c (- d) - d (c - d)

$c \cdot c + c (- d) - d (c - d)$

Step 2.3

Apply the distributive property.

c \cdot c + c (- d) - d c - d (- d)

$c \cdot c + c (- d) - d c - d (- d)$

c \cdot c + c (- d) - d c - d (- d)

$c \cdot c + c (- d) - d c - d (- d)$

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

c

$c$ by

c

$c$ .

c^{2} + c (- d) - d c - d (- d)

$c^{2} + c (- d) - d c - d (- d)$

Step 3.1.2

Rewrite using the commutative property of multiplication.

c^{2} - c d - d c - d (- d)

$c^{2} - c d - d c - d (- d)$

Step 3.1.3

Rewrite using the commutative property of multiplication.

c^{2} - c d - d c - 1 \cdot - 1 d \cdot d

$c^{2} - c d - d c - 1 \cdot - 1 d \cdot d$

Step 3.1.4

Multiply

d

$d$ by

d

$d$ by adding the exponents.

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Step 3.1.4.1

Move

d

$d$ .

c^{2} - c d - d c - 1 \cdot - 1 (d \cdot d)

$c^{2} - c d - d c - 1 \cdot - 1 (d \cdot d)$

Step 3.1.4.2

Multiply

d

$d$ by

d

$d$ .

c^{2} - c d - d c - 1 \cdot - 1 d^{2}

$c^{2} - c d - d c - 1 \cdot - 1 d^{2}$

c^{2} - c d - d c - 1 \cdot - 1 d^{2}

$c^{2} - c d - d c - 1 \cdot - 1 d^{2}$

Step 3.1.5

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

c^{2} - c d - d c + 1 d^{2}

$c^{2} - c d - d c + 1 d^{2}$

Step 3.1.6

Multiply

d^{2}

$d^{2}$ by

1

$1$ .

c^{2} - c d - d c + d^{2}

$c^{2} - c d - d c + d^{2}$

c^{2} - c d - d c + d^{2}

$c^{2} - c d - d c + d^{2}$

Step 3.2

Subtract

d c

$d c$ from

- c d

$- c d$ .

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Step 3.2.1

Move

d

$d$ .

c^{2} - c d - 1 c d + d^{2}

$c^{2} - c d - 1 c d + d^{2}$

Step 3.2.2

Subtract

c d

$c d$ from

- c d

$- c d$ .

c^{2} - 2 c d + d^{2}

$c^{2} - 2 c d + d^{2}$

c^{2} - 2 c d + d^{2}

$c^{2} - 2 c d + d^{2}$

c^{2} - 2 c d + d^{2}

$c^{2} - 2 c d + d^{2}$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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