Solve (x+5)(x-4x-3i)(x-4x+3i)

$$( x + 5 ) ( x - 4 x - 3 i ) ( x - 4 x + 3 i )$$

Evaluate

$$-9\left(x+5\right)\left(-x^{2}-1\right)$$

Solution Steps

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

$$\left(x+5\right)\left(-3x-3i\right)\left(x-4x+3i\right)$$

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

$$\left(x+5\right)\left(-3x-3i\right)\left(-3x+3i\right)$$

Apply the distributive property by multiplying each term of x+5 by each term of -3x-3i.

$$\left(-3x^{2}-3ix-15x-15i\right)\left(-3x+3i\right)$$

Combine -3ix and -15x to get \left(-15-3i\right)x.

$$\left(-3x^{2}+\left(-15-3i\right)x-15i\right)\left(-3x+3i\right)$$

Apply the distributive property by multiplying each term of -3x^{2}+\left(-15-3i\right)x-15i by each term of -3x+3i.

$$9x^{3}-9ix^{2}+\left(45+9i\right)x^{2}+\left(9-45i\right)x+45ix+45$$

Combine -9ix^{2} and \left(45+9i\right)x^{2} to get 45x^{2}.

$$9x^{3}+45x^{2}+\left(9-45i\right)x+45ix+45$$

Combine \left(9-45i\right)x and 45ix to get 9x.

$$9x^{3}+45x^{2}+9x+45$$

Expand

$$9x^{3}+45x^{2}+9x+45$$

Solution Steps

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

$$\left(x+5\right)\left(-3x-3i\right)\left(x-4x+3i\right)$$

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

$$\left(x+5\right)\left(-3x-3i\right)\left(-3x+3i\right)$$

Apply the distributive property by multiplying each term of x+5 by each term of -3x-3i.

$$\left(-3x^{2}-3ix-15x-15i\right)\left(-3x+3i\right)$$

Combine -3ix and -15x to get \left(-15-3i\right)x.

$$\left(-3x^{2}+\left(-15-3i\right)x-15i\right)\left(-3x+3i\right)$$

Apply the distributive property by multiplying each term of -3x^{2}+\left(-15-3i\right)x-15i by each term of -3x+3i.

$$9x^{3}-9ix^{2}+\left(45+9i\right)x^{2}+\left(9-45i\right)x+45ix+45$$

Combine -9ix^{2} and \left(45+9i\right)x^{2} to get 45x^{2}.

$$9x^{3}+45x^{2}+\left(9-45i\right)x+45ix+45$$

Combine \left(9-45i\right)x and 45ix to get 9x.

$$9x^{3}+45x^{2}+9x+45$$