# Multiply (x-(5-2i))(x-(5+2i)) (x-(5-2i))(x-(5+2i))
Simplify terms.
Simplify each term.
Apply the distributive property.
(x-1⋅5-(-2i))(x-(5+2i))
Multiply -1 by 5.
(x-5-(-2i))(x-(5+2i))
Multiply -2 by -1.
(x-5+2i)(x-(5+2i))
(x-5+2i)(x-(5+2i))
Simplify each term.
Apply the distributive property.
(x-5+2i)(x-1⋅5-(2i))
Multiply -1 by 5.
(x-5+2i)(x-5-(2i))
Multiply 2 by -1.
(x-5+2i)(x-5-2i)
(x-5+2i)(x-5-2i)
(x-5+2i)(x-5-2i)
Expand (x-5+2i)(x-5-2i) by multiplying each term in the first expression by each term in the second expression.
x⋅x+x⋅-5+x(-2i)-5x-5⋅-5-5(-2i)+2ix+2i⋅-5+2i(-2i)
Simplify terms.
Combine the opposite terms in x⋅x+x⋅-5+x(-2i)-5x-5⋅-5-5(-2i)+2ix+2i⋅-5+2i(-2i).
Reorder the factors in the terms x(-2i) and 2ix.
x⋅x+x⋅-5-2ix-5x-5⋅-5-5(-2i)+2ix+2i⋅-5+2i(-2i)
x⋅x+x⋅-5+0-5x-5⋅-5-5(-2i)+2i⋅-5+2i(-2i)
x⋅x+x⋅-5-5x-5⋅-5-5(-2i)+2i⋅-5+2i(-2i)
x⋅x+x⋅-5-5x-5⋅-5-5(-2i)+2i⋅-5+2i(-2i)
Simplify each term.
Multiply x by x.
x2+x⋅-5-5x-5⋅-5-5(-2i)+2i⋅-5+2i(-2i)
Move -5 to the left of x.
x2-5⋅x-5x-5⋅-5-5(-2i)+2i⋅-5+2i(-2i)
Multiply -5 by -5.
x2-5x-5x+25-5(-2i)+2i⋅-5+2i(-2i)
Multiply -2 by -5.
x2-5x-5x+25+10i+2i⋅-5+2i(-2i)
Multiply -5 by 2.
x2-5x-5x+25+10i-10i+2i(-2i)
Multiply 2i(-2i).
Multiply -2 by 2.
x2-5x-5x+25+10i-10i-4ii
Raise i to the power of 1.
x2-5x-5x+25+10i-10i-4(i1i)
Raise i to the power of 1.
x2-5x-5x+25+10i-10i-4(i1i1)
Use the power rule aman=am+n to combine exponents.
x2-5x-5x+25+10i-10i-4i1+1
x2-5x-5x+25+10i-10i-4i2
x2-5x-5x+25+10i-10i-4i2
Rewrite i2 as -1.
x2-5x-5x+25+10i-10i-4⋅-1
Multiply -4 by -1.
x2-5x-5x+25+10i-10i+4
x2-5x-5x+25+10i-10i+4
Combine the opposite terms in x2-5x-5x+25+10i-10i+4.
Subtract 10i from 10i.
x2-5x-5x+25+0+4
x2-5x-5x+25+4
x2-5x-5x+25+4
Subtract 5x from -5x.
x2-10x+25+4