Question

The table shows the area of two rugs a preschool teacher has in her room. She places the two rugs together to make one big rug. What is the area in square units of the new rug in factored form?

Answer 1

Given:

The area of the blue rug is:

$8(x+\frac{1}{2})$

And the area of the red rug is :

$10(x+\frac{2}{5})$

So, the area of both of them is the sum of the given areas:

So, the total area =

$\begin{gathered} 8(x+\frac{1}{2})+10(x+\frac{2}{5}) \\ =8x+8\cdot\frac{1}{2}+10x+10\cdot\frac{2}{5} \\ =8x+4+10x+4 \\ =18x+8 \\ =2(9x+4) \end{gathered}$

so, the area of the new rug in factored form = 2 ( 9x + 4 )