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x^{2}-5x-2ix-5x+25+10i+2ix-10i+4
Apply the distributive property by multiplying each term of x-5+2i by each term of x-5-2i.
x^{2}-5x-2ix-5x+2ix+25+4+\left(10-10\right)i
Combine the real and imaginary parts.
x^{2}-5x-2ix-5x+2ix+29
Do the additions.
x^{2}+\left(-5-2i\right)x-5x+2ix+29
Combine -5x and -2ix to get \left(-5-2i\right)x.
x^{2}+\left(-10-2i\right)x+2ix+29
Combine \left(-5-2i\right)x and -5x to get \left(-10-2i\right)x.
x^{2}-10x+29
Combine \left(-10-2i\right)x and 2ix to get -10x.
x^{2}-5x-2ix-5x+25+10i+2ix-10i+4
Apply the distributive property by multiplying each term of x-5+2i by each term of x-5-2i.
x^{2}-5x-2ix-5x+2ix+25+4+\left(10-10\right)i
Combine the real and imaginary parts.
x^{2}-5x-2ix-5x+2ix+29
Do the additions.
x^{2}+\left(-5-2i\right)x-5x+2ix+29
Combine -5x and -2ix to get \left(-5-2i\right)x.
x^{2}+\left(-10-2i\right)x+2ix+29
Combine \left(-5-2i\right)x and -5x to get \left(-10-2i\right)x.
x^{2}-10x+29
Combine \left(-10-2i\right)x and 2ix to get -10x.