## Algebra 1

$9x^{2}$-24x+16
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