Question

1. write an expression for the area of the shaded region in the figure at the left, and simplify the result. (section p.3)
2. ______________

Explanation:

Step1: Find area of large - rectangle

The length of the large rectangle is $2x+(x + 1)=3x + 1$ and the width is $3x+1$. So the area of the large rectangle $A_{1}=(3x + 1)^2=9x^{2}+6x + 1$.

Step2: Find area of small - rectangle

The length of the small rectangle is $2x$ and the width is $2x$. So the area of the small rectangle $A_{2}=2x\times2x = 4x^{2}$.

Step3: Find area of shaded region

The area of the shaded region $A=A_{1}-A_{2}$. Substitute $A_{1}$ and $A_{2}$ into the formula: $A=(9x^{2}+6x + 1)-4x^{2}=5x^{2}+6x + 1$.

Answer:

$5x^{2}+6x + 1$