How do you multiply and simplify #\frac { 2c + 5} { c ^ { 2} + 4c + 4} \cdot \frac { c ^ { 4} + 4c ^ { 3} + 4c ^ { 2} } { 2c + 5}#?

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Answer 1 · 2018-05-12T10:52:44

# c^2 #

Factoring:

#=> (2c+5)/(c^2 + 4c + 4 ) * ( c^2 ( c^2 + 4c + 4 ) ) / (2c+5) #

#=> ( (2c+5) c^2 ( c^2 + 4c + c ) ) / ( (c^2 + 4c + 4 )(2c+5 ) ) #

Canceling down :

#=> ( cancel((2c+5)) c^2 ( c^2 + 4c + c ) ) / ( (c^2 + 4c + 4 )cancel((2c+5 ) ) #

#=> ( c^2 ( c^2 + 4c + c ) ) / ( (c^2 + 4c + 4 ) ) #

#=> ( c^2 cancel(( c^2 + 4c + c )) ) / ( cancel((c^2 + 4c + 4 ) ) #

# = c^2 #