Question 825541
Let x = the length of a side of the original square. 
Then the original area is: {{{x^2}}}
And the length of the side of the expanded square would be: x+4
Then the area of the expanded square would be: {{{(x+4)^2}}}<br>
With one variable we only need one equation to solve the problem. "When the side of a square is increased by four units, its area is increased by 80 square units." can be reworded as "the area of the expanded square is 80 square units more than the area of the original square." This reworded is probably easier to translate into:
{{{(x+4)^2 = x^2 + 80}}}
Now we solve. First we simplify:
{{{x^2+8x+16 = x^2 + 80}}}
Subtracting {{{x^2}}} from each side:
{{{8x+16 = 80}}}
Subtracting 16 from each side:
{{{8x = 64}}}
Dividing both sides by 8:
{{{x = 8}}}
Since x is the length of the side of the original square and since that is what the problem asks for, we are finished.