Evaluate
\left(a-ib\right)\left(a+b\right)
Expand
a^{2}+\left(1-i\right)ab-ib^{2}
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a\left(a-ib\right)+1b\left(a-ib\right)
Use the distributive property to multiply a+1b by a-ib.
a^{2}-iab+1b\left(a-ib\right)
Use the distributive property to multiply a by a-ib.
a^{2}-iab+1ba-ib^{2}
Use the distributive property to multiply 1b by a-ib.
a^{2}+\left(1-i\right)ab-ib^{2}
Combine -iab and 1ba to get \left(1-i\right)ab.
a\left(a-ib\right)+1b\left(a-ib\right)
Use the distributive property to multiply a+1b by a-ib.
a^{2}-iab+1b\left(a-ib\right)
Use the distributive property to multiply a by a-ib.
a^{2}-iab+1ba-ib^{2}
Use the distributive property to multiply 1b by a-ib.
a^{2}+\left(1-i\right)ab-ib^{2}
Combine -iab and 1ba to get \left(1-i\right)ab.
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