Answer
$9x^{2}$-24x+16
Work Step by Step
A square contains 4 equal sides, and the formula for the area of a square is:
A=$s^{2}$, where A=the area of the square and s=the length of a side
Since one side of the square has a length of 3x-4, the other 3 sides of the square have lengths of 3x-4 because a square contains 4 equal sides. Therefore, 3x-4=s. If we substitute 3x-4 in for s in the area formula, we can figure out what polynomial represents the area of the base of the birdhouse.
A=$s^{2}$, s=3x-4,
A=$(3x-4)^{2}$
Now, we apply the rule that states that
$(a-b)^{2}$=$a^{2}$-2ab+$b^{2}$, and set a=3x and b=4
Therefore,
A=$(3x-4)^{2}$=$(3x)^{2}$-2(3x)(4)+$4^{2}$
=$9x^{2}$-24x+16
