Answer
$2(4x+5)^2(5x+1)(50x+31)$
Work Step by Step
The given expression is
$3(4x+5)^2\cdot 4(5x+1)^2+(4x+5)^3\cdot 2(5x+1)\cdot 5$
$=12(4x+5)^2(5x+1)^2+10(4x+5)^3(5x+1)$
Factor out $2(4x+5)^2(5x+1)$.
$=2(4x+5)^2(5x+1)[6(5x+1)+5(4x+5)]$
Use distributive property.
$=2(4x+5)^2(5x+1)[30x+6+20x+25]$
Add like terms.
$=2(4x+5)^2(5x+1)(50x+31)$
Hence, the completely factored form of the given expression is $2(4x+5)^2(5x+1)(50x+31)$.
