Basic Math Examples

$a (b + c) = d c$

Step 1

Simplify $a (b + c)$ .

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Step 1.1

Rewrite.

$0 + 0 + a (b + c) = d c$

Step 1.2

Simplify by adding zeros.

$a (b + c) = d c$

Step 1.3

Apply the distributive property.

$a b + a c = d c$

Step 2

Subtract $d c$ from both sides of the equation.

$a b + a c - d c = 0$

Step 3

Subtract $a b$ from both sides of the equation.

$a c - d c = - a b$

Step 4

Factor $c$ out of $a c - d c$ .

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Step 4.1

Factor $c$ out of $a c$ .

$c a - d c = - a b$

Step 4.2

Factor $c$ out of $- d c$ .

$c a + c (- d) = - a b$

Step 4.3

Factor $c$ out of $c a + c (- d)$ .

$c (a - d) = - a b$

Step 5

Divide each term in $c (a - d) = - a b$ by $a - d$ and simplify.

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Step 5.1

Divide each term in $c (a - d) = - a b$ by $a - d$ .

$\frac{c (a - d)}{a - d} = \frac{- a b}{a - d}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $a - d$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{c (a - d)}{a - d} = \frac{- a b}{a - d}$

Step 5.2.1.2

Divide $c$ by $1$ .

$c = \frac{- a b}{a - d}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$c = - \frac{a b}{a - d}$