Algebra Examples

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

Step 1

Simplify $a (y + c)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + a (y + c) = b (y - c)$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify $b (y - c)$ .

Tap for more steps...

Step 2.1

Apply the distributive property.

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

Step 2.2

Rewrite using the commutative property of multiplication.

$a y + a c = b y - b c$

Step 3

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

$a y + a c - b y = - b c$

Step 4

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

$a y - b y = - b c - a c$

Step 5

Factor $y$ out of $a y - b y$ .

Tap for more steps...

Step 5.1

Factor $y$ out of $a y$ .

$y a - b y = - b c - a c$

Step 5.2

Factor $y$ out of $- b y$ .

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

Step 5.3

Factor $y$ out of $y a + y (- b)$ .

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

Step 6

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

Tap for more steps...

Step 6.1

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

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

Step 6.2

Simplify the left side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of $a - b$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Divide $y$ by $1$ .

$y = \frac{- b c}{a - b} + \frac{- a c}{a - b}$

Step 6.3

Simplify the right side.

Tap for more steps...

Step 6.3.1

Combine the numerators over the common denominator.

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

Step 6.3.2

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

Tap for more steps...

Step 6.3.2.1

Factor $c$ out of $- b c$ .

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

Step 6.3.2.2

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

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

Step 6.3.2.3

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

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

Step 6.3.3

Factor $- 1$ out of $- b$ .

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

Step 6.3.4

Factor $- 1$ out of $- a$ .

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

Step 6.3.5

Factor $- 1$ out of $- (b) - (a)$ .

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

Step 6.3.6

Simplify the expression.

Tap for more steps...

Step 6.3.6.1

Rewrite $- (b + a)$ as $- 1 (b + a)$ .

$y = \frac{c (- 1 (b + a))}{a - b}$

Step 6.3.6.2

Move the negative in front of the fraction.

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