Algebra Examples

$(a, b)$ , $(c, d)$

Step 1

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

$\sqrt{{(c - a)}^{2} + {(d - b)}^{2}}$

Step 3

Simplify.

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Step 3.1

Rewrite ${(c - a)}^{2}$ as $(c - a) (c - a)$ .

$\sqrt{(c - a) (c - a) + {(d - b)}^{2}}$

Step 3.2

Expand $(c - a) (c - a)$ using the FOIL Method.

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Step 3.2.1

Apply the distributive property.

$\sqrt{c (c - a) - a (c - a) + {(d - b)}^{2}}$

Step 3.2.2

Apply the distributive property.

$\sqrt{c \cdot c + c (- a) - a (c - a) + {(d - b)}^{2}}$

Step 3.2.3

Apply the distributive property.

$\sqrt{c \cdot c + c (- a) - a c - a (- a) + {(d - b)}^{2}}$

Step 3.3

Simplify and combine like terms.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Multiply $c$ by $c$ .

$\sqrt{c^{2} + c (- a) - a c - a (- a) + {(d - b)}^{2}}$

Step 3.3.1.2

Rewrite using the commutative property of multiplication.

$\sqrt{c^{2} - c a - a c - a (- a) + {(d - b)}^{2}}$

Step 3.3.1.3

Rewrite using the commutative property of multiplication.

$\sqrt{c^{2} - c a - a c - 1 \cdot - 1 a \cdot a + {(d - b)}^{2}}$

Step 3.3.1.4

Multiply $a$ by $a$ by adding the exponents.

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Step 3.3.1.4.1

Move $a$ .

$\sqrt{c^{2} - c a - a c - 1 \cdot - 1 (a \cdot a) + {(d - b)}^{2}}$

Step 3.3.1.4.2

Multiply $a$ by $a$ .

$\sqrt{c^{2} - c a - a c - 1 \cdot - 1 a^{2} + {(d - b)}^{2}}$

Step 3.3.1.5

Multiply $- 1$ by $- 1$ .

$\sqrt{c^{2} - c a - a c + 1 a^{2} + {(d - b)}^{2}}$

Step 3.3.1.6

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

$\sqrt{c^{2} - c a - a c + a^{2} + {(d - b)}^{2}}$

Step 3.3.2

Subtract $a c$ from $- c a$ .

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Step 3.3.2.1

Move $c$ .

$\sqrt{c^{2} - a c - a c + a^{2} + {(d - b)}^{2}}$

Step 3.3.2.2

Subtract $a c$ from $- a c$ .

$\sqrt{c^{2} - 2 a c + a^{2} + {(d - b)}^{2}}$

Step 3.4

Rewrite ${(d - b)}^{2}$ as $(d - b) (d - b)$ .

$\sqrt{c^{2} - 2 a c + a^{2} + (d - b) (d - b)}$

Step 3.5

Expand $(d - b) (d - b)$ using the FOIL Method.

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Step 3.5.1

Apply the distributive property.

$\sqrt{c^{2} - 2 a c + a^{2} + d (d - b) - b (d - b)}$

Step 3.5.2

Apply the distributive property.

$\sqrt{c^{2} - 2 a c + a^{2} + d \cdot d + d (- b) - b (d - b)}$

Step 3.5.3

Apply the distributive property.

$\sqrt{c^{2} - 2 a c + a^{2} + d \cdot d + d (- b) - b d - b (- b)}$

Step 3.6

Simplify and combine like terms.

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Step 3.6.1

Simplify each term.

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Step 3.6.1.1

Multiply $d$ by $d$ .

$\sqrt{c^{2} - 2 a c + a^{2} + d^{2} + d (- b) - b d - b (- b)}$

Step 3.6.1.2

Rewrite using the commutative property of multiplication.

$\sqrt{c^{2} - 2 a c + a^{2} + d^{2} - d b - b d - b (- b)}$

Step 3.6.1.3

Rewrite using the commutative property of multiplication.

$\sqrt{c^{2} - 2 a c + a^{2} + d^{2} - d b - b d - 1 \cdot - 1 b \cdot b}$

Step 3.6.1.4

Multiply $b$ by $b$ by adding the exponents.

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Step 3.6.1.4.1

Move $b$ .

$\sqrt{c^{2} - 2 a c + a^{2} + d^{2} - d b - b d - 1 \cdot - 1 (b \cdot b)}$

Step 3.6.1.4.2

Multiply $b$ by $b$ .

$\sqrt{c^{2} - 2 a c + a^{2} + d^{2} - d b - b d - 1 \cdot - 1 b^{2}}$

Step 3.6.1.5

Multiply $- 1$ by $- 1$ .

$\sqrt{c^{2} - 2 a c + a^{2} + d^{2} - d b - b d + 1 b^{2}}$

Step 3.6.1.6

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

$\sqrt{c^{2} - 2 a c + a^{2} + d^{2} - d b - b d + b^{2}}$

Step 3.6.2

Subtract $b d$ from $- d b$ .

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Step 3.6.2.1

Move $d$ .

$\sqrt{c^{2} - 2 a c + a^{2} + d^{2} - b d - b d + b^{2}}$

Step 3.6.2.2

Subtract $b d$ from $- b d$ .

$\sqrt{c^{2} - 2 a c + a^{2} + d^{2} - 2 b d + b^{2}}$