Simplify (16x-x^2)(4+ square root of x)

$(16 x - x^{2}) (4 + \sqrt{x})$

Step 1

Expand $(16 x - x^{2}) (4 + \sqrt{x})$ using the FOIL Method.

Apply the distributive property.

$16 x (4 + \sqrt{x}) - x^{2} (4 + \sqrt{x})$

Apply the distributive property.

$16 x \cdot 4 + 16 x \sqrt{x} - x^{2} (4 + \sqrt{x})$

Apply the distributive property.

$16 x \cdot 4 + 16 x \sqrt{x} - x^{2} \cdot 4 - x^{2} \sqrt{x}$

Step 2

Simplify terms.

Simplify each term.

Multiply $4$ by $16$ .

$64 x + 16 x \sqrt{x} - x^{2} \cdot 4 - x^{2} \sqrt{x}$

Multiply $4$ by $- 1$ .

$64 x + 16 x \sqrt{x} - 4 x^{2} - x^{2} \sqrt{x}$

Simplify the expression.

Move $16 x \sqrt{x}$ .

$64 x - 4 x^{2} + 16 x \sqrt{x} - x^{2} \sqrt{x}$

Reorder $64 x$ and $- 4 x^{2}$ .

$- 4 x^{2} + 64 x + 16 x \sqrt{x} - x^{2} \sqrt{x}$