Question 104673
{{{(5a-3b)^2}}}
{{{(5a-3b)(5a-3b)}}}
{{{(5a+(-3b))(5a+(-3b))}}}
Use the FOIL method (First, Outer, Inner, Last)
First {{{(highlight(5a) + (-3b)) (highlight(5a) + (-3b))}}} : {{{5a*5a}}}
Outer {{{(highlight(5a) + (-3b)) (5a + highlight((-3b)))}}} : {{{5a*(-3b)}}}
Inner {{{(5a + highlight(-3b)) (highlight(5a) +(-3b))}}} : {{{(-3b)*5a}}}
Last {{{(5a + highlight(-3b)) (5a + highlight((-3b)))}}} :{{{(-3b)*(-3b)}}}
{{{(5a-3b)^2}}}=First + Outer + Inner + Last
{{{(5a-3b)^2=5a*5a+5a*(-3b)+(-3b)*5a+(-3b)*(-3b)}}}
{{{(5a-3b)^2=25a^2-15ab-15ab+9b^2}}}
{{{(5a-3b)^2=25a^2-30ab+9b^2}}}
A faster way is to compare to the following equation
{{{(X+Y)^2=X^2+2XY+Y^2}}}
where 
{{{X=5a}}} and {{{Y=-3b}}}
{{{(5a-3b)^2=(5a)^2+2(5a)(-3b)+(-3b)^2}}}
{{{(5a-3b)^2=25a^2-30ab+9b^2}}}