Solve left(x+2right)^2left(-3x-3ixright)left(-3x+3ixright)

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

$$\left(x^{2}+4x+4\right)\left(-3x-3ix\right)\left(-3x+3ix\right)$$

Combine -3x and -3ix to get \left(-3-3i\right)x.

$$\left(x^{2}+4x+4\right)\left(-3-3i\right)x\left(-3x+3ix\right)$$

Combine -3x and 3ix to get \left(-3+3i\right)x.

$$\left(x^{2}+4x+4\right)\left(-3-3i\right)x\left(-3+3i\right)x$$

Multiply -3-3i and -3+3i to get 18.

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

Multiply x and x to get x^{2}.

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

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

$$\left(18x^{2}+72x+72\right)x^{2}$$

Use the distributive property to multiply 18x^{2}+72x+72 by x^{2}.

$$18x^{4}+72x^{3}+72x^{2}$$

Expand

$$18x^{4}+72x^{3}+72x^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

$$\left(x^{2}+4x+4\right)\left(-3x-3ix\right)\left(-3x+3ix\right)$$

Combine -3x and -3ix to get \left(-3-3i\right)x.

$$\left(x^{2}+4x+4\right)\left(-3-3i\right)x\left(-3x+3ix\right)$$

Combine -3x and 3ix to get \left(-3+3i\right)x.

$$\left(x^{2}+4x+4\right)\left(-3-3i\right)x\left(-3+3i\right)x$$

Multiply -3-3i and -3+3i to get 18.

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

Multiply x and x to get x^{2}.

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

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

$$\left(18x^{2}+72x+72\right)x^{2}$$

Use the distributive property to multiply 18x^{2}+72x+72 by x^{2}.

$$18x^{4}+72x^{3}+72x^{2}$$