Question 784498
{{{9x^2=(3x)^2}}}
{{{25=5^2}}}
The perfect square trinomial is the square of binomial {{{3x+5}}}
The missing term is
{{{2*(3x)*(5)=highlight(30x)}}}
 
The square of a sum (like {{{3x}}}{{{"+"}}}{{{5}}})
is the sum of the two squares (in this case {{{(3x)^2}}} and {{{5^2}}})
plus "two rectangles" (twice the product of the squared terms).
It is what you do in real life when you make a square larger:
{{{drawing(300,300,-2.8,5.2,-2.8,5.2,
rectangle(0,0,3.95,3.95),
green(rectangle(-0.05,0,-1.95,3.95)),
green(rectangle(0,-0.05,3.95,-1.95)),
blue(rectangle(-0.05,-0.05,-1.95,-1.95)),
red(rectangle(-2,-2,4,4)),
locate(-1.9,-0.8,blue(a)),locate(-1,-0.05,blue(a)),locate(-1,-0.6,blue(a^2)),
locate(2,3.9,b),locate(0.1,2,b),locate(2,2.2,b^2),
locate(1.7,-1,green(ab)),locate(-1.3,2,green(ab)),
locate(0.6,-2,red(a+b)),locate(4.05,1.2,red(a+b)),
red(arrow(0.5,-2.2,-2,-2.2)),red(arrow(1.5,-2.2,4,-2.2)),
red(arrow(4.3,0.5,4.3,-2)),red(arrow(4.3,1.5,4.3,4)),
locate(-1.5,5,red((a+b)^2)),locate(0,4.8,"="),
locate(1,5,a^2),locate(1.7,4.8, "+2"),locate(2.2,4.8,green(ab)),
locate(2.8,4.8, "+"),locate(3.2,5,blue(b^2))
)}}}