Pre-Algebra Examples

$\frac{4}{9} \cdot (36 x^{2} + 45 x + 18)$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Apply the distributive property.

$\frac{4}{9} (36 x^{2}) + \frac{4}{9} (45 x) + \frac{4}{9} \cdot 18$

Step 1.2

Simplify.

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Step 1.2.1

Cancel the common factor of $9$ .

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Step 1.2.1.1

Factor $9$ out of $36 x^{2}$ .

$\frac{4}{9} (9 (4 x^{2})) + \frac{4}{9} (45 x) + \frac{4}{9} \cdot 18$

Step 1.2.1.2

Cancel the common factor.

$\frac{4}{9} (9 (4 x^{2})) + \frac{4}{9} (45 x) + \frac{4}{9} \cdot 18$

Step 1.2.1.3

Rewrite the expression.

$4 (4 x^{2}) + \frac{4}{9} (45 x) + \frac{4}{9} \cdot 18$

Step 1.2.2

Multiply $4$ by $4$ .

$16 x^{2} + \frac{4}{9} (45 x) + \frac{4}{9} \cdot 18$

Step 1.2.3

Cancel the common factor of $9$ .

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Step 1.2.3.1

Factor $9$ out of $45 x$ .

$16 x^{2} + \frac{4}{9} (9 (5 x)) + \frac{4}{9} \cdot 18$

Step 1.2.3.2

Cancel the common factor.

$16 x^{2} + \frac{4}{9} (9 (5 x)) + \frac{4}{9} \cdot 18$

Step 1.2.3.3

Rewrite the expression.

$16 x^{2} + 4 (5 x) + \frac{4}{9} \cdot 18$

Step 1.2.4

Multiply $5$ by $4$ .

$16 x^{2} + 20 x + \frac{4}{9} \cdot 18$

Step 1.2.5

Cancel the common factor of $9$ .

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Step 1.2.5.1

Factor $9$ out of $18$ .

$16 x^{2} + 20 x + \frac{4}{9} \cdot (9 (2))$

Step 1.2.5.2

Cancel the common factor.

$16 x^{2} + 20 x + \frac{4}{9} \cdot (9 \cdot 2)$

Step 1.2.5.3

Rewrite the expression.

$16 x^{2} + 20 x + 4 \cdot 2$

Step 1.2.6

Multiply $4$ by $2$ .

$16 x^{2} + 20 x + 8$

Step 2

The largest exponent is the degree of the polynomial.

$2$