Given:
The area of the blue rug is:
[tex]8(x+\frac{1}{2})[/tex]
And the area of the red rug is :
[tex]10(x+\frac{2}{5})[/tex]
So, the area of both of them is the sum of the given areas:
So, the total area =
[tex]\begin{gathered} 8(x+\frac{1}{2})+10(x+\frac{2}{5}) \\ =8x+8\cdot\frac{1}{2}+10x+10\cdot\frac{2}{5} \\ =8x+4+10x+4 \\ =18x+8 \\ =2(9x+4) \end{gathered}[/tex]
so, the area of the new rug in factored form = 2 ( 9x + 4 )
