Solve (2sqrt{x+2})[(2x^2-18)(sqrt{x+2})]

$$( 2 \sqrt { x + 2 } ) [ ( 2 x ^ { 2 } - 18 ) ( \sqrt { x + 2 } ) ]$$

Evaluate

$$4\left(x+2\right)\left(x^{2}-9\right)$$

Solution Steps

Multiply \sqrt{x+2} and \sqrt{x+2} to get \left(\sqrt{x+2}\right)^{2}.

$$2\left(\sqrt{x+2}\right)^{2}\left(2x^{2}-18\right)$$

Calculate \sqrt{x+2} to the power of 2 and get x+2.

$$2\left(x+2\right)\left(2x^{2}-18\right)$$

Use the distributive property to multiply 2 by x+2.

$$\left(2x+4\right)\left(2x^{2}-18\right)$$

Use the distributive property to multiply 2x+4 by 2x^{2}-18.

$$4x^{3}-36x+8x^{2}-72$$

Factor

$$4\left(x-3\right)\left(x+2\right)\left(x+3\right)$$