Multiply (1+3i)(5+i)\left(1 + 3 i\right) \left(5 + i\right) using FOIL

The calculator will expand the product of binomials (1+3i)(5+i)\left(1 + 3 i\right) \left(5 + i\right) using the FOIL method, with steps shown.

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Your Input

Multiply (1+3i)(5+i)\left(1 + 3 i\right) \left(5 + i\right) using FOIL.

Solution

((1)+(3i))((5)+(i))=(1)(5)First+(1)(i)Outer+(3i)(5)Inner+(3i)(i)Last=5+i+15i3=2+16i\left({\color{red}\left(1\right)} + {\color{purple}\left(3 i\right)}\right) \left({\color{green}\left(5\right)} + {\color{blue}\left(i\right)}\right) = \underbrace{{\color{red}\left(1\right)} {\color{green}\left(5\right)}}_{\text{First}} + \underbrace{{\color{red}\left(1\right)} {\color{blue}\left(i\right)}}_{\text{Outer}} + \underbrace{{\color{purple}\left(3 i\right)} {\color{green}\left(5\right)}}_{\text{Inner}} + \underbrace{{\color{purple}\left(3 i\right)} {\color{blue}\left(i\right)}}_{\text{Last}} = 5 + i + 15 i - 3 = 2 + 16 i

Answer

(1+3i)(5+i)=2+16i\left(1 + 3 i\right) \left(5 + i\right) = 2 + 16 iA