How do you multiply #(v - 3) ( 4v + 2)#?

2 Answers
Neha M.
Feb 2, 2017

#4v^2-10v-6#

Explanation:

This is an extremely simple question that uses the algebraic property of distribution. You must 'distribute' separately each of the terms of the first factor with the second factor as shown below:

#(v-3)(4v+2)#
#= (v*(4v+2))+(-3*(4v+2))#
#= (4v^2+2v)+(-12v-6)#
#= 4v^2+2v-12v-6#
#= 4v^2-10v-6#

Jim G.
Feb 2, 2017

#4v^2-10v-6#

Explanation:

Each term in the second bracket must be multiplied by each term in the first bracket, as shown below.

#(color(red)(v-3))(4v+2)#

#=color(red)(v)(4v+2)color(red)(-3)(4v+2)#

distribute.

#=4v^2+2v-12v-6#

collect like terms.

#=4v^2-10v-6#

An alternative method is called FOIL. This is illustrated in the diagram.
enter image source here

#"Firsts "vxx4v=4v^2#

#"Outers " 2xxv=2v#

#" Inners " -3xx4v=-12v#

#"Lasts " -3xx2=-6#

Add together and simplify.

#4v^2+2v-12v-6=4v^2-10v-6#

With practice, this method can be faster to do than the method above.

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