Answer
$3((3x+5)^{2}$)
Work Step by Step
Given the polynomial
$27x^{2}$ + 90x + 75
We see that all three terms have a common factor of 3, so we factor out the 3.
3($9x^{2}$ + 90x + 25)
We see that the polynomial has the first and last term squared and the middle term is -2 times the first and last term. Thus it follows the rule of
$a^{2}$ - 2ab + $b^{2}$ = $(a-b)^{2}$
3($(3x)^{2}$ + 90x + $5^{2}$)
In this polynomial a= 3x and b=5
3($3x^{2}$ + 90x + $5^{2}$) = $3((3x+5)^{2}$)
