12)
well, the picture has a length of (x + 2.5) and a width of (x).
if we extend the picture 1 inch on all sides, it'll end up like the picture below.
[tex]\bf (1+x+2.5+1)(1+x+1)\implies (x+4.5)(x+2)\implies \stackrel{\mathbb{FOIL}}{x^2+6.5x+9}[/tex]
13)
let's find the area of the larger rectangle, that includes the smaller rectangle, and then let's find the area of the smaller rectangle, and after subtracting the smaller area from the larger area, what's leftover is the shaded region.
[tex]\bf \stackrel{\textit{larger area}}{(9x)(6x)}-\stackrel{\textit{smaller area}}{(3x-2)(4x)}\implies 54x^2-(12x^2-8x) \\\\\\ 54x^2-12x^2+8x\implies 42x^2+8x[/tex]
14)
we'll do the same thing here as we did in 13)
[tex]\bf \stackrel{\textit{larger area}}{(4x+3)(2x+2)}-\stackrel{\textit{smaller area}}{(x+5)(x+1)}\implies \stackrel{FOIL}{8x^2+14x+6}~~-~~\stackrel{FOIL}{(x^2+6x+5)} \\\\\\ 8x^2+14x+6~~~~-~~x^2-6x-5\implies 7x^2+8x+1[/tex]
