Algebra Examples

$(9 x - x^{2}) (3 + \sqrt{x})$

Step 1

Expand $(9 x - x^{2}) (3 + \sqrt{x})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$9 x (3 + \sqrt{x}) - x^{2} (3 + \sqrt{x})$

Step 1.2

Apply the distributive property.

$9 x \cdot 3 + 9 x \sqrt{x} - x^{2} (3 + \sqrt{x})$

Step 1.3

Apply the distributive property.

$9 x \cdot 3 + 9 x \sqrt{x} - x^{2} \cdot 3 - x^{2} \sqrt{x}$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $3$ by $9$ .

$27 x + 9 x \sqrt{x} - x^{2} \cdot 3 - x^{2} \sqrt{x}$

Step 2.1.2

Multiply $3$ by $- 1$ .

$27 x + 9 x \sqrt{x} - 3 x^{2} - x^{2} \sqrt{x}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $9 x \sqrt{x}$ .

$27 x - 3 x^{2} + 9 x \sqrt{x} - x^{2} \sqrt{x}$

Step 2.2.2

Reorder $27 x$ and $- 3 x^{2}$ .

$- 3 x^{2} + 27 x + 9 x \sqrt{x} - x^{2} \sqrt{x}$