Question #473e0

1 Answer
Douglas K.
Oct 24, 2017

You can multiply one of the binomials by 4 and then use F.O.I.L. or you can use F.O.I.L to multiply the binomials and then multiply by 4; I recommend the latter.

Explanation:

Given: #4(5+2i)(5+2i)#

Option 1: Multiply one of the binomials by 4 and the use. F.O.I.L.

Multiply the first binomial by 4:

#(20+8i)(5+2i)#

#100 + 40i + 40i + 16i^2#

Substitute -1 for #i^2#:

#100 + 40i + 40i - 16#

Combine like terms:

#84 + 80i#

Option 2: Use. F.O.I.L. to multiply the binomials and then multiply by 4.

#4(25 + 10i + 10i + 4i^2)#

Substitute -1 for #i^2#:

#4(25 + 10i + 10i - 4)#

Combine like terms:

#4(21 + 20i)#

Multiply by 4:

#84+80i#

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