Algebra Examples

$\frac{4}{9} a (18 b - 9 c + 27)$

Step 1

Apply the distributive property.

$\frac{4}{9} \cdot (a (18 b) + a (- 9 c) + a \cdot 27)$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$\frac{4}{9} \cdot (18 a b + a (- 9 c) + a \cdot 27)$

Step 2.2

Rewrite using the commutative property of multiplication.

$\frac{4}{9} \cdot (18 a b - 9 a c + a \cdot 27)$

Step 2.3

Move $27$ to the left of $a$ .

$\frac{4}{9} \cdot (18 a b - 9 a c + 27 \cdot a)$

Step 3

Apply the distributive property.

$\frac{4}{9} (18 a b) + \frac{4}{9} (- 9 a c) + \frac{4}{9} (27 a)$

Step 4

Simplify.

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Step 4.1

Cancel the common factor of $9$ .

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Step 4.1.1

Factor $9$ out of $18 a b$ .

$\frac{4}{9} (9 (2 a b)) + \frac{4}{9} (- 9 a c) + \frac{4}{9} (27 a)$

Step 4.1.2

Cancel the common factor.

$\frac{4}{9} (9 (2 a b)) + \frac{4}{9} (- 9 a c) + \frac{4}{9} (27 a)$

Step 4.1.3

Rewrite the expression.

$4 (2 a b) + \frac{4}{9} (- 9 a c) + \frac{4}{9} (27 a)$

Step 4.2

Multiply $2$ by $4$ .

$8 (a b) + \frac{4}{9} (- 9 a c) + \frac{4}{9} (27 a)$

Step 4.3

Cancel the common factor of $9$ .

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Step 4.3.1

Factor $9$ out of $- 9 a c$ .

$8 (a b) + \frac{4}{9} (9 (- a c)) + \frac{4}{9} (27 a)$

Step 4.3.2

Cancel the common factor.

$8 (a b) + \frac{4}{9} (9 (- a c)) + \frac{4}{9} (27 a)$

Step 4.3.3

Rewrite the expression.

$8 (a b) + 4 (- a c) + \frac{4}{9} (27 a)$

Step 4.4

Multiply $- 1$ by $4$ .

$8 (a b) - 4 (a c) + \frac{4}{9} (27 a)$

Step 4.5

Cancel the common factor of $9$ .

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Step 4.5.1

Factor $9$ out of $27 a$ .

$8 (a b) - 4 (a c) + \frac{4}{9} (9 (3 a))$

Step 4.5.2

Cancel the common factor.

$8 (a b) - 4 (a c) + \frac{4}{9} (9 (3 a))$

Step 4.5.3

Rewrite the expression.

$8 (a b) - 4 (a c) + 4 (3 a)$

Step 4.6

Multiply $3$ by $4$ .

$8 (a b) - 4 (a c) + 12 a$

Step 5

Remove parentheses.

$8 a b - 4 a c + 12 a$