Answer
$-4x^2+25y^2-12x-9$
Work Step by Step
The given expression is of the form $(a-b)(a+b)$ where $a=5y$ and $b=2x+3$
RECALL:
(1) $(a-b)(a+b) = a^2-b^2$
(2) $(a+b)^2=a^2+2ab+b^2$
Multiply the expression using formula (1) above to obtain:
$=(5y)^2 - (2x+3)^2
\\=25y^2-(2x+3)^2$
Square the binomial using formula (2) with $a=2x$ and $b=3$ above to obtain:
$=25y^2-[(2x)^2+2(2x)(3)+3^2]
\\=25y^2-(4x^2+12x+9)$
Subtract each term of the trinomial to obtain:
$=25y^2-4x^2-12x-9
\\=-4x^2+25y^2-12x-9$
