Solve (1-2x)(x+2)(1+2x)

$$( 1 - 2 x ) ( x + 2 ) ( 1 + 2 x )$$

Evaluate

$$\left(x+2\right)\left(1-4x^{2}\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 1-2x by each term of x+2.

$$\left(x+2-2x^{2}-4x\right)\left(1+2x\right)$$

Combine x and -4x to get -3x.

$$\left(-3x+2-2x^{2}\right)\left(1+2x\right)$$

Apply the distributive property by multiplying each term of -3x+2-2x^{2} by each term of 1+2x.

$$-3x-6x^{2}+2+4x-2x^{2}-4x^{3}$$

Combine -3x and 4x to get x.

$$x-6x^{2}+2-2x^{2}-4x^{3}$$

Combine -6x^{2} and -2x^{2} to get -8x^{2}.

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

Expand

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

Solution Steps

Apply the distributive property by multiplying each term of 1-2x by each term of x+2.

$$\left(x+2-2x^{2}-4x\right)\left(1+2x\right)$$

Combine x and -4x to get -3x.

$$\left(-3x+2-2x^{2}\right)\left(1+2x\right)$$

Apply the distributive property by multiplying each term of -3x+2-2x^{2} by each term of 1+2x.

$$-3x-6x^{2}+2+4x-2x^{2}-4x^{3}$$

Combine -3x and 4x to get x.

$$x-6x^{2}+2-2x^{2}-4x^{3}$$

Combine -6x^{2} and -2x^{2} to get -8x^{2}.

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