How do you multiply and simplify #\frac { 20v ^ { 4} + 28v ^ { 3} + 8v ^ { 2} } { 20v ^ { 3} + 8v ^ { 2} } \cdot \frac { 3v ^ { 2} - 10v + 7} { v - 1}#?

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Answer 1 · 2018-01-28T21:21:58

#3v^2-4v-7#

I simplified multipliers

#(20v^4+28v^3+8v^2)/(20v^3+8v^2)#

=#[4v^2*(5v^2+7v+2)]/[4v^2*(5v+2)]#

=#(5v^2+7v+2)/(5v+2)#

=#[(5v+2)*(v+1)]/(5v+2)#

=#v+1# and,

#(3v^2-10v+7)/(v-1)#

=#[(3v-7)*(v-1)]/(v-1)#

=#3v-7#

Thus,

#(20v^4+28v^3+8v^2)/(20v^3+8v^2)#*#(3v^2-10v+7)/(v-1)#

=#(v+1)*(3v-7)#

=#3v^2-4v-7#