Solve (x+0)(x-2+5i)(x-2-5i)

$$( x + 0 ) ( x - 2 + 5 i ) ( x - 2 - 5 i )$$

Evaluate

$$x\left(x+\left(-2-5i\right)\right)\left(x+\left(-2+5i\right)\right)$$

Solution Steps

Anything plus zero gives itself.

$$x\left(x-2+5i\right)\left(x-2-5i\right)$$

Use the distributive property to multiply x by x-2+5i.

$$\left(x^{2}-2x+5ix\right)\left(x-2-5i\right)$$

Combine -2x and 5ix to get \left(-2+5i\right)x.

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

Apply the distributive property by multiplying each term of x^{2}+\left(-2+5i\right)x by each term of x-2-5i.

$$x^{3}-2x^{2}-5ix^{2}+\left(-2+5i\right)x^{2}+\left(4-10i\right)x+\left(25+10i\right)x$$

Combine -2x^{2} and -5ix^{2} to get \left(-2-5i\right)x^{2}.

$$x^{3}+\left(-2-5i\right)x^{2}+\left(-2+5i\right)x^{2}+\left(4-10i\right)x+\left(25+10i\right)x$$

Combine \left(-2-5i\right)x^{2} and \left(-2+5i\right)x^{2} to get -4x^{2}.

$$x^{3}-4x^{2}+\left(4-10i\right)x+\left(25+10i\right)x$$

Combine \left(4-10i\right)x and \left(25+10i\right)x to get 29x.

$$x^{3}-4x^{2}+29x$$

Expand

$$x^{3}-4x^{2}+29x$$

Solution Steps

Anything plus zero gives itself.

$$x\left(x-2+5i\right)\left(x-2-5i\right)$$

Use the distributive property to multiply x by x-2+5i.

$$\left(x^{2}-2x+5ix\right)\left(x-2-5i\right)$$

Combine -2x and 5ix to get \left(-2+5i\right)x.

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

Apply the distributive property by multiplying each term of x^{2}+\left(-2+5i\right)x by each term of x-2-5i.

$$x^{3}-2x^{2}-5ix^{2}+\left(-2+5i\right)x^{2}+\left(4-10i\right)x+\left(25+10i\right)x$$

Combine -2x^{2} and -5ix^{2} to get \left(-2-5i\right)x^{2}.

$$x^{3}+\left(-2-5i\right)x^{2}+\left(-2+5i\right)x^{2}+\left(4-10i\right)x+\left(25+10i\right)x$$

Combine \left(-2-5i\right)x^{2} and \left(-2+5i\right)x^{2} to get -4x^{2}.

$$x^{3}-4x^{2}+\left(4-10i\right)x+\left(25+10i\right)x$$

Combine \left(4-10i\right)x and \left(25+10i\right)x to get 29x.

$$x^{3}-4x^{2}+29x$$